How can I fix a not-quite-hole in my carpet?
You might try crocheting yarn from elsewhere on the carpet onto the backing. Basically you are pushing loops of yarn through that backing and then pulling them up so they're even with the rest of the yarn. It'll be finicky to get looking right, but should be a nice durable solution if done well.

Alternately, as others have said, cut a scrap and use it to patch that area. If you match the nap direction and keep the edges of the backing material tight when you tape it in place, you should be able to tease the strands up enough to make it look seamless.