I was in a similar situation too. I accidentally jumped on the head of one of my pet chinchillas. I wasn't sure what to do, and more than freaked out. It took a few minutes to die, but fortunately it wasn't too prolonged.
Later on, someone suggested that if you don't have the stomach to kill the animal with your hands - or want to avoid a mess - you should put the animal in a bag, and hook it up to the tail pipe of your car.
It's not the most pleasant way to die, but if you're squeamish like me and can't bring yourself to provide a more hands on death, the gassing is an option better than prolonged suffering.