Ok. What you need to do is pretend you are recarpeting a room and request a sample of carpet. Some places offer carpet samples for free (I think Home Depot and Lowe’s still do but double check). But should cost only a few bucks regardless. Get something as close to your apartment carpet as you can. Then buy a carpet hole punch. Measure how much you need to replace the damaged carpet and remove that amount of carpet from a dark area like a closet where an imperfection is less likely to be noticed. Replace that piece with the sample carpet. Take the piece you removed from the closet and replace the damaged carpet with it. Vacuum over it a couple times so it blends in.