I have an injured mouse in a trap. What should I do?

This is horrible, so faint of heart, please stay away. The mouse is caught in a household trap supposed to provide a quick death (called 'a better mousetrap'). The problem is that it didn't get a chance to stick the whole head in there before it snapped - so the mouse didn't die and has an injured face. It's currently in a tupperware container. It's a wild mouse, not a pet (a pest, in fact). Can I kill it quickly and (relatively) humanely? How? I don't know anybody with a snake (a preferred solution). Advice?