To this day, I feel bad about a mouse that I tried to save, close to 30 years ago. My GF at the time was crying when I got to her house, and it was because her stepdad had used one of the sticky traps to catch a mouse. I hate those things, because it seems like such a bad way to go. We took it outside, and tried everything we could think of to free it, but we couldn't get it done and the mouse died. I don't think about it often, but often enough that I only get live capture traps if I need them.
I don't see feeling bad about this as a character flaw - I think it means that you don't want to cause death and/or suffering for no reason, and that's a good thing. There is a difference between this and killing an animal for food - everything must eat, and eating other creatures is one way to fulfill that requirement. In this case, you weren't killing the mouse for food, you were killing it because it had invaded your space and was interfering with your life. Nothing wrong with that - mice can carry disease, and keeping them away from our living space is important in stopping the spread of some diseases. But to balance the guilt with still wanting to ensure that you keep them away, go with a live capture one, don't forget it's there, and release them somewhere they have a decent shot at living.