Should I feel bad that I killed a mouse?

I always used the ones where you capture them and release them outside. But it got to a point where they kept coming back over and over again and my mom and dad said we had to kill em. So we set the snap traps and I heard the clap and one died. I felt so bad! Cause its little body was just laying there and.. uhh. I;m a very sentsitive person when it comes to animals. So should I feel bad that I killed one?