Admitting to a mistake is especially likely to draw positive benefits if it is coupled with

I believe the answer is:  An offer to rectify the situation

Offering to rectify the situation that is caused by mistake would most likely taken as an indicator that you're being honest about your apology and truly want to get things right between you and the victim.
In such situation, the victim would most likely empathize with your effort and forgive you.

What’s the