How do I help an injured frog?

It looks like it has one hand almost competely missing and very mangled, it somehow found its way to my garden even though I dont have pond. I have made a makeshift small pond for him out of a paella pan with rocks and plant pots and it is in amoungst the veggies for safety. He seems happy enough but not moving much.. how do you know if it is in pain from losing a hand? will it heal or should we put him out of his misery? If I was alone and had lost my hand I would probably want to die!!!!!