Petri pretty much swallows things whole, so most of the time I just feed him in his tank.
I had the same... uh, problem... with carrots. Try making thinner pieces, like with a vegetable peeler.
Petri's escaped a few times. Since he's in such a small tank, I didn't want to take out any water. I made a little wall with index cards and "laminated" it with packing tape.