Regret is a complex emotion. You feel guilt about something in the past which makes you feel all the more guilty because you can't change it.
It's not a useless emotion. It's you realizing something now you didn't realize then. That being the case, you aren't likely to repeat it.
I do have a solution. From a story I heard.
Jesus said: "A man was going down from Jerusalem to Jericho, when he fell into the hands of robbers. They stripped him of his clothes, beat him and went away, leaving him half dead. A priest happened to be going down the same road, and when he saw the man, he passed by on the other side. So too, a Levite, when he came to the place and saw him, passed by on the other side. But a Samaritan, as he traveled, came where the man was; and when he saw him, he took pity on him. He went to him and bandaged his wounds, pouring on oil and wine. Then he put the man on his own donkey, took him to an inn and took care of him. The next day he took out two silver cins and gave them to the innkeeper. 'Look after him,' he said, 'and when I return, I will reimburse you for any extra expense you may have.' "Which of these three do you think was a neighbor to the man who fell into the hands of robbers?"
The expert in the law replied, "The one who had mercy on him."
Jesus told him, "Go and do likewise."
Background- Samaritans and Jews generally despised one another, as in hated. Yet here one decided to do something to help another at his own expense. Did he have to? No, and in fact walking right by and spitting on the injured man would be expected.
What has this to do with your problem? You can never change the past, only the now and future. Do someone good who needs it. It won't erase the past, but you will accumulate satisfaction which will more than offset regret.
The Samaritan did a good thing.
Go and do likewise.