It depends on how the fight started or what it was about. If it was a fight over an inconsequential thing, then it makes sense to not bother further about something which is inconsequential. However it does make sense to figure out why you were fighting over a stupid thing.
What were you arguing over? Do you feel the issue is still unresolved? And why are you fighting so much lately?
Never regret anything that has happened in your life. It cannot be changed, forgotten or undone. So, take it as a lesson learned and move on.