I think the root cause of regret with a woman after a break-up is the idea that somehow a man did something wrong. That is only things had been different it would have turned out better.
The key to long term happiness and getting over someone fast is to admit to yourself that it had nothing to do with you, it was all her and things just were not meant to be.
Now there are times when a man is at fault (gambling, alcoholism, drug addition, lying, cheating, weak @ss behavior), and when this happens, and it is your fault... chalk it up to a painful lesson, learn from that and move on to the next with a promise to yourself you will not make the same errors. If you just cannot fix yourself, go get some counseling. Men do have the power to change. But thinking you can go back and fix things with a woman that you messed up with is not realistic. It's like the late great Doc Love once said "You can't go back, you are not starting with a clean slate... you have a dirty slate."