It depends on what, exactly, you mean by image quality. In terms of ghosting or flare caused by reflections on the back surfaces of the elements of a lens this is often the case. If the ghosting is visible through the viewfinder when the mirror is down and the shutter closed on a DSLR, then the ghosting is not being caused by the light bouncing off the front of the sensor. With a traditionally designed DSLR, if the ghosting is only visible in the photo taken but not in the viewfinder beforehand, then the source of the initial reflection is likely the IR filter in front of the sensor. The light that reflects off the front of the sensor must then bounce back from another surface forward in the optical path with enough intensity to be detected by the sensor. This could be either the uncoated back of a lens element or the uncoated back of a filter attached to the lens.
In general many lenses, especially those considered consumer grade, that were designed during the film era were not expected to perform at the same level lenses designed more recently for use in digital cameras are expected to. This applies not only in terms of lens coatings to reduce internal reflections, but also in terms of things like resolution, chromatic aberration, and distortion. Most film photos taken with consumer lenses were printed uncropped with very little darkroom adjustment made to the image. In contrast, after the digital revolution even shots made with compact point and shoot cameras and camera phones are routinely cropped and heavily processed. This has placed a demand for higher performance in even consumer grade lenses. Advances in materials and lens design, aided by the explosion of the processing capacity of super computers to simulate different ideas without the days, weeks, or even months needed to produce an actual prototype, have continued to advance the quality of not only premium lenses but consumer grade lenses as well.
This does not mean that it is always a compromise to use a lens made during the film era on a digital camera, nor does it mean that all lenses designed during the film era are inferior to any lens made specifically for digital. It is certainly possible to produce outstanding images using older lenses. But there are times, such as photographing a very dark scene containing a few bright light sources, when the advantages of well designed modern lenses will be evident.
Here's a link with drawings that illustrate the different kinds of flare. Ghosting caused by reflections off the film or sensor are the last type discussed. Thanks to @D3C4FF for the link in regard to another question.
Here's an image that illustrates what happens when you use a lens designed in the film era with a digital DSLR. As you can plainly see, the bright lights in the upper left corner of the image are ghosted in the lower left corner.