Heinze wanted to leave United after falling behind Patrice Evra in the pecking order at Old Trafford.
The Marseille defender will face his former club in the Champions League on Wednesday.
Heinze said: "I don't have many regrets from my career as a footballer, but that episode with Ferguson has to be one of them. I'm impulsive and strong-willed and this has got me into trouble at times, which was the case at the time when I left United.
"I regret it a lot, especially the last month. I am strong personality and so is Alex Ferguson. But it was my decision to leave, I took the decision.
"I hope the way I left won't tarnish the fans' view of me. I spent three wonderful years in Manchester."