I had the same problem when making felted slippers for my grand children. I went to Hobby Lobby and bought Safe-T back rug backing. It costs about $9.99 It is a liquid (about the substance of glue.) I put it on the bottom with a foam brush, let it dry a few hours, did another coat, then let it dry 24 hours. It works great, so far I've done 5 pairs of slipper bottoms, and I have only used about half of what is in the container. Since felted slippers don't go in the laundry, I'm not sure how the backing hold up in the washer and dryer. The instructions say to not wash the item it is applied to for 2 weeks. I think that like the puff paint, it would break down after awhile, on second thought, not sure I would put it in the dryer at all.
Hope this helps.