So sorry to hear about this - absolutely heartbreaking. Try placing a small dish of water near the site. It may or may not be too late for the little frog. I don't know what the humidity is where you live but maybe there is a chance there is enough humidity for the frog to survive a short time. I've found that small froglets tend to hide most of the time so it might not come out.
About your cat - I do not think eating the tiny frog will do anything to your cat (they eat worse things), but you might want to keep the cat out of the room for a short time because the cat will see it and eat it before you have a chance to react.
For future note - I always place the deli cup in the vivarium then lift the lid. Usually the froglets will jump right out but if they don't I leave the cup in the vivarium until they decide to get out
Again, so sorry this happened but please do not allow this to discourage you. This is a wonderful hobby and very rewarding. This forum is a great place to gather info and feedback.