Yes, as most anemones do, can, and will eat fish, carpets are really good at it. Most fish its accidental specially if there new to the tank and don't know the lay of the land. Also a new entry to the tank could be skittish and accidentally dart into the anemone meeting its fate....I once had 3 saddle back clowns (ed, edd, and eddy) and a large carpet easily 10in around. Well every time we would attempt to put a new arrival in the tank we would have to supple silver sides too. The clown fish (mainly the dom) would come up grab the silver side and take it to the anemone and shove it in feeding it. she would also do this to new arrivals unless tricked with a silver side...Though bubble tips are not normally fish snatchers their tentacles do carry stinging harpoons which will stun and kill the fish and the fish will get wrapped up and consumed.
Did you notice your anemone looking any different after your fish disappeared? like was it a little more deflated maybe looked like it was just opening back up? Maybe a little fatter and happier?