it's still an animal.

They deserve it.
I had to take a tiny lizard (fence lizard) just 4" long to the vets, take a mite sample and treat him for a couple of months. this lizard cost me nothing, and is'nt worth much but i'd never leave an animal to suffer.
i had to have my mouse put down two weeks ago.
good luck with yours!! Your so nice to do this for you mouse, most people would'nt bother.