Yes, he really did regret it. While he injured me is a weak attempt at an excuse, he follows it with "I killed my mother's son. I killed my father's son." and breaks down in tears. No reason to think he is anything but sincere.

Also telling is the subsequent conversation with Connie. When Michael tells her he made confession and how much it meant to him ("He changed things."), Connie immediately references Fredo's death. She seemed to know that it had been weighing on Michael's conscience.