While Michael may have regretted killing Fredo by the time he confessed to Lamberto, at the time, it was necessary that Michael kill Fredo. Michael was the head of a criminal empire, and when traitors and enemies got in the way it was mandatory they be killed. Anything short of that would be a sign of weakness, at least in Michael's mind. I am sure if he had asked Tom Hagen for advice on this issue Tom would have come up with some kind of arrangement that allowed Fredo to live.