The moon is a fairly easy object to photograph. There are a few things that are helpful to know up front. As no specific lens example or photographic example was offered, I can only offer general thoughts based on many of the sample photos that I've seen from those who are new to astrophotography (specifically lunar imaging).
Everyone starts somewhere and I certainly have my share of poor quality images. Don't think of those images as a tragic waste. Instead, think of them as an investment in learning.
Size: Undersampling or excessive cropping?
The angular width of the moon is roughly 1/2°. The moon's distance from Earth varies a little throughout the month, so it's angular width varies a little. But it's generally about 1/2° from edge to edge.
At about 1/2°, it would just barely squeeze into the frame of an APS-C sensor camera if imaged with an 1800mm focal length. Although a focal length a bit closer to 1200mm is probably a more comfortable fit in the frame. A 300mm zoom is fairly common, but that would provide a horizontal field of view of about 2.9° to 3.1° depending on if your camera has a 1.6x vs. 1.5x crop factor. A 150-600mm zoom or a 2x teleconverter would be helpful (or a 150-600 with a 2x adapter). Otherwise you'll be cropping aggressively.
By subpar prime, I'm imaging a consumer-grade zoom - possibly up to 250mm or 300mm focal length. This will require heavy cropping. Aggressive cropping will magnify any imperfections, such as slightly soft focus.
Exposure: Is it correct?
I often see moon exposures that are poorly exposed - most often overexposed. I've come to attribute this to trusting the camera's built-in metering for exposure.
The average surface albedo of the moon is 0.12 (12% reflectivity) - this is roughly the reflectivity of an old asphalt road (not fresh-laid asphalt).
While the moon is lit by the Sun, you are looking through a lot of atmosphere and that eats up a bit of the light. The technical term for this is atmospheric extinction. The exact amount of light depends on how high the moon is above the horizon. If the moon were at zenith you would be looking through 1x atmosphere. If the moon is lower near the horizon you may be looking at 5x atmospheres or more.
The simple formula for the moon is the Looney 11 rule-of-thumb. This is similar to the Sunny 16 rule-of-thumb but modified for the moon. Looney 11 says that if you shoot at f/11 then the correct shutter duration should be the inverse of the ISO. In other words: at f/11 & ISO 100, use 1/100th sec exposure. At f/11 & ISO 200, use 1/200th, etc.
You do not have to use f/11. You can trade stops of aperture for shutter speed. But the formula is based on f/11 because that's the only f-stop where the shutter speed will be the direct inverse of the ISO.
Do not trust or use camera metering. It will likely be fooled by the amount of blackness surrounding the moon. Using Looney 11 will result in a better exposure. If in doubt, check the histogram. You may see black clipping on the left edge of the histogram and that's ok. The sky is mostly dark and the histogram should accurately represent that. Avoid any clipping on the right-edge which indicates overexposure.
Earth is moving:
The Earth rotates from West to East at an angular speed of just barely more than 15 arc-seconds per second. The moon's size is roughly 30 arc-minutes. Thus the moon will move in the sky by roughly its own width in about 2 minutes. You can use an angular field-of-view (FoV) calculator to determine the FoV of your lens and a bit of math to determine how that translates with respect to pixels.
Since the exposure for the moon is usually 1/100th sec or faster, in just 1/100th sec the moon moves .15 arc-seconds. If you take longer exposures to capture earthshine on the dark parts of the moon, then the exposure time can lead to a blurred result. But for exposures capturing the lit area of the moon, exposure duration and the rotation of the Earth are likely not a problem.
One major issue of sub-par lenses are the optical flaws. One issue of note is chromatic aberration (CA) which is also sometimes called color fringing. When light passes through any refractive surface, such as a lens, light waves will bend when they hit each air/glass surface - one at the front of each element and another at the back of each element. Glass has a desirable property called refraction which focuses the light but also comes with an undesirable property called dispersion which splits the light apart into its constituent wavelengths. Shorter, higher-energy waves bend more than longer, lower-energy waves. Basically "blue" light bends more strongly than "red" light.
In the visible spectrum, roughly 400nm to 700nm, the blue light is near the 400nm end, green is nearer to the middle, and red is nearer to the longer 700nm end.
Light passing nearly the the center axis of the lens won't bend as much because at that point the glass doesn't have much of an angle as the light hits it. It enters and exits nearly straight-on to the glass. Nearer to the edges and corners, the curvature is stronger and the color fringing (a/k/a CA) tends to be more apparent with a blue-fringe on one edge of an object and a red-fringe on the opposite edge. This is the light beginning to spread into a "rainbow" - but only just starting. You only see the edges of the rainbow spectrum but not the full spectrum of colors.
This is caused by different wavelengths of light focusing at different distances. If the sensor were just a bit nearer to the lens "blue" light would be focused better but "green" and especially "red" would be a little worse. If focused a little farther from the sensor, "red" would enjoy better focus but the "blue" end of the spectrum would be missing focus. Basically the "blue", "green", and "red" portions of the spectrum are not focusing at the same distance.
Software often allows you to adjust for chromatic aberration. It works slightly resizing the red, green, and blue channels so that they converge and you achieve slightly better focus.
I own (but usually do not use) a green filter to attenuate the red & blue channels. Since the moon is largely a monochrome subject - it's actually loaded with color if you really intensify the saturation - you can eliminate color fringing with an appropriate filter.
Higher quality lenses usually employ higher quality materials, such as one or more elements of fluorite crystal, which have low-dispersion properties. These exotic materials are expensive and typically not used in consumer priced lenses. They also often employ additional elements to better correct for dispersion.
I tend to avoid shooting a full or near-full moon unless it's part of a larger composition of a night-scape scene. If a full moon is in the image on it's own it will appear flat.
Like so many other areas of photography, subjects illuminated by light from the side looks better than light from straight on. For the moon, this translates to its phase. Taking the moon near first or last quarter will provide illumination from an angle so you'll get nice 3D texture in mountains and craters created by the highlights and shadows. Taking the image near a full moon will result in a flat image that looks 2D.
This image was shot using a 540mm f/5.4 telescope (a TeleVue NP101is) using a 2x adapter (TeleVue PowerMate ... a telecentric focal length multiplier) which brings this to 1080mm at f/10.8 (basically f/11). The image is not cropped. A Canon 60Da camera with an APS-C sensor was used. This single image was taken using ISO 100 and is a 1/100th sec. exposure at f/11. Lightroom was used to adjust contrast and apply some sharpening.
Much sharper results can be achieved using "stacking" techniques but that's another topic.
In lunar, solar, or planetary imaging, atmospheric seeing conditions will play a role, especially with planetary imaging. The atmosphere behaves a bit like a lens of its own. Twinkling stars are a result of atmospheric scintillation in which turbulence, often in the upper atmosphere, is disturbing air density and creating distortions. This reduces the crispness of the image. Keep in mind that in most traditional photography, the camera is shooting through anywhere from several feet of air to perhaps a few miles of air. We generally do not shoot through several hundreds of miles of air. This reduces image quality in a way that is not the fault of your optical instrument.
Imagine looking at a coin the bottom of a pool of completely calm water. You can easily see the coin. If you used something - perhaps binoculars - to magnify the image you might even be able to read details on the coin. Now imagine some waves in the pool. You can see the coin, but it keeps distorting. No amount of magnification is likely to ever give you a clear-crisp view of the coin. That is what astronomers are referring to when they talk about seeing.
To combat atmospheric distortions, shoot on nights of good seeing conditions. If stars low in the sky are twinkling more than normal then that's a strong indicator that seeing conditions are poor.
Second, image stacking can be used. This involves shooting hundreds of images and using software to combine the results. Astrophotographers often use cameras in video mode to do this. Usually they want raw uncompressed video frames. Most cameras' movie modes use compressed frames that lack the data to achieve great results.
In addition to reducing the effects of atmospheric turbulence, image stacking can also reduce the effects of image noise.
There is some free planetary stacking software such as AutoStakkert and Registax. There are also paid stacking programs for sale. These applications align the edges of the disc of a planet or the moon and also look for features of contrast that can be used to align the frames. They judge the quality of each frame and help you select only the best frames to combine while rejecting poor quality frames. The stacked result is often noticeably sharper than any single frame. Like everything else in photography there is a bit of a learning curve. But there are also loads of free tutorial videos on how to use the software to achieve great results.