Well, really, the Punisher was created based on the old Bronson "Death Wish" movies from the 80's. Based on that, you have two possible ways for him to react to hurting a civilian:
1) He feels momentary regret, but the world is a hard place and he can't stop pursuing the greater good.
2) Frank is so driven by trauma to eradicate criminals that he's incapable of perceiving "civilians" once he gets his guns out. He will rationalize that everyone he shot had it coming somehow or another.