Double sided tape has a drawback. Well, it has two drawbacks.
- It falls off when you least want it to do so.
- It sticks like crazy when you want to remove it.
Having said that, you probably tore off more than just a layer of paint. I'll bet you actually tore off the surface layer of paper on the drywall.
Can you repair this by just painting over the spot? Well, it depends. Will anyone ever look at it? Sorry, but it will be painfully obvious what you did. So this depends on how critical the observer is. If I was your landlord and I saw a poorly done patch when you were moving out, I'd mutter a few obscenities under my breath, then quietly mention to you about how you just forfeited your security deposit.
The problem is that paint won't match that well. The color difference will be obvious. Plus, due to the hole in the surface, there will be small shadows that will be quite obvious, so you will need to fill in the surface so it is smooth, BEFORE painting. Anyway, if you tried to paint in just that small area with a brush, one would easily see the texture differences from painting with a brush compared to what was an original roller applied paint surface.
All of this means you really will need to spackle over the hole, feathering it out over the surface of the wall at least a few inches in each direction, and then sand smooth. Once you have done this far enough out, repainting the entire wall will make sense anyway.
Lessons to be learned:
- Either don't use double sided tape,
- or, be much more careful removing it if you do. This usually means to use a solvent that will break down the adhesive, but not the surface of your wall. They sell stuff to do this, usually called something like Goo-Gone. Another solvent that often works is rubbing alcohol. It evaporates quickly, and does not attack paint, although it will harm some surfaces like shellac. Always test any solvent on a small, inconspicuous spot before using it. And watch out for fumes, so use good ventilation.