How to make up for a mistake?

Today I made a mistake, a huge mistake. It was purely an accident and not caused by carelessness, it was just a confluence of events. Anyway, because of my mistake someone else is suffering. I feel horrible about it and have apologized, even though it truly was just an accident. No one has been physically harmed, this person is just going to have to go through some trials for the next couple of days because of it. What do you do when you feel like sorry isn’t enough?