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I have been out taking some evening photos (just after sunset) and I have noticed that in a number of instances the higher f numbers ( 14+ ) are appearing more blurred than the lower f numbers ( < 14). I use a tripod and take a wide range of photos so I have been comparing the same photo with different f stops.

I am using a Nikon D3000 and begin by framing the photo and then setting the F Stop and adjusting the apature based upon the meter on the camera display. I use a tripod so I was expecting the majority of images to come out sharp. I was wondering if I may have set the F stop too high and not let enough light in.

For example, a photo taken at 62mm focal length at f/14 is appearing more sharp than an image taken at the same focal length and at f/22.

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You've hit the diffraction limit. That link has some amazing answers with a lot of detail, so I won't be redundant, but in short, once the aperture gets to be below certain physical size, diffraction causes inevitable blur. For your camera (and any other camera with an APS-C-sized sensor), the limit is a little beyond f/11.

The amount of light let in doesn't really matter. If that's the case, your image will be underexposed, but this effect will happen in either case.

The bad news is: you can't really do anything about this. But, you might still get an overall benefit in across-the-frame sharpness — the overall sharpness may be a bit lower, but near and far details may be closer in sharpness giving a more unified appearance. See Do smaller apertures provide more depth of field past the diffraction limit, even if peak sharpness suffers? for more.

The good news is: you now know your equipment better, and can decide if sharpness of the point of focus is more or less important than depth of field for a given scene.

Also, if your goal in stopping down is actually to take a longer exposure in bright light, take a look at What are neutral density filters and how do I use them to create long exposures in daylight?

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    No, it's nothing to do with quality. It's a property of physics that no amount of money can get around. However, a more expensive camera will help in one way: a larger sensor means longer focal length for the same field of view, which in turn means a larger physical aperture for the same f-stop. But that particular gain is rather minimal (effectively allowing you one more stop), and going to a larger sensor is a very big step up in price. – Please Read Profile Jan 9 '13 at 18:22
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    The diffraction limit is why "mega pixel wars" are so stupid. Marketing folks love to brag about how many mega-pixels they have, but that does not mean that they take better pictures. We want better pixels, not more of them. When the pixels get small, they have their own diffraction issues, in addition to the issues that @mattdm talks about for the lens. – Pat Farrell Jan 9 '13 at 20:01
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    As it happens, we have a Q/A on the megapixel discussion: photo.stackexchange.com/questions/14773/… – Please Read Profile Jan 9 '13 at 22:32
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    A larger sensor does not really help with diffraction as your depth of field will be shallower due to the larger physical aperture. Thus you could achieve the same depth of field / diffraction without a more expensive camera by simply opening the aperture on your current camera. And maximum apertures for 35mm system lenses tend to be wider than medium / large format... – Matt Grum Jan 10 '13 at 14:54
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    on aps-c in the 10-12MP times it kicked in between F8 and F11. On FF between F11 and F16. On the current cameras with higher res it kicks in between F5.6 and F8 on aps-c and F8 - F11 on FF. Ill update my post with links to compare. – Michael Nielsen Jan 10 '13 at 16:57
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You can only avoid it by avoiding to use the small aperture, or by getting a camera with larger sensor (such as a 12MP full frame, which can handle at least ~F11, maybe even F14). Your 10MP crop sensor can handle down to ~F/9. If the depth of field is fine but the exposure is too much, use a ND filter.

If the DOF is too narrow you are in trouble. You have to use the tilt on a tilt-shift lens, or have to accept the diffraction "glow" effect.

10MP Aps-c comparison F8 and F11:

http://www.the-digital-picture.com/Reviews/ISO-12233-Sample-Crops.aspx?Lens=253&Camera=396&Sample=0&FLI=0&API=5&LensComp=253&CameraComp=396&SampleComp=0&FLIComp=0&APIComp=6

Current "insane resolution" cameras (2013):

APS-C: F5.6 -> F8 (notice diffraction)

http://www.the-digital-picture.com/Reviews/ISO-12233-Sample-Crops.aspx?Lens=253&Camera=736&Sample=0&FLI=0&API=4&LensComp=253&CameraComp=736&SampleComp=0&FLIComp=0&APIComp=5

FullFrame F8 -> F16 diffraction:

http://www.the-digital-picture.com/Reviews/ISO-12233-Sample-Crops.aspx?Lens=253&Camera=453&Sample=0&FLI=0&API=5&LensComp=253&CameraComp=453&SampleComp=0&FLIComp=0&APIComp=6

Here you can calculate the limit for your camera:

http://www.cambridgeincolour.com/tutorials/diffraction-photography.htm

The first one applies to the pixel peeping approach that I used to get very strict limits above.

The second calculator looks at if it is visible if the pictures end up the same size print (10x8 inch) and then the limit only changes with sensor size, not sensor resolution and the limits for crop remain at F11, and FF can go all the way to F22.

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