Strachan, now the manager of Coventry City, was angered by Ferguson's attack on him in his autobiography Managing My Life. But Ferguson, the manager at United, insisted he had given a truthful account of his dealings with the former Scotland player at Aberdeen and United.
"He was a great player at Aberdeen," Ferguson said. "But you have to balance it out by the experiences I had with him, and I think I've done that," he said in a BBC radio interview.
Strachan is one of a number of managers and former players to come under fire from Ferguson in his autobiography, which could yet land him in hot water with the League Managers' Association, although the chief executive John Barnwell was tight-lipped yesterday over claims that they may censure their most powerful member.
"I am absolutely furious this has been leaked today of all days," he said. "I am not saying anything at the moment until we have had discussions with various people."
Meanwhile, the South African international midfielder Quinton Fortune has completed his move to United after being issued with a work permit. Fortune has signed a four-year contract at Old Trafford following his transfer from Atletico Madrid in a deal worth a reported pounds 1.5m.
The midfielder, a member of South Africa's 1998 World Cup squad, was too late to play in the match at Coventry and has also been ruled out of tomorrow's European Super Cup encounter with Lazio in Monaco. The first game he is eligible for is the Bank Holiday Monday encounter with Newcastle United at Old Trafford.
Ferguson moved for Fortune after he impressed in a recent trial at the club and he believes he will prove to be a useful recruit to his already vast squad. Fortune is eligible for Europe and turned down a move to the Spanish side Real Valladolid to come to United.
Ferguson is also continuing his efforts to sign a defender before next week's Champions' League transfer deadline following the news that Ronny Johnsen requires surgery on his knees. Also, Wes Brown fears he may yet need an operation on his cruciate ligaments injury, although the England defender has made good progress in the month since he suffered the injury during a pre-season friendly.
Initially United feared Brown would be out for the season, but he is on course to play some part in the campaign. He has ditched his crutches and is doing light work at the Cliff training ground to the delight of United's medical team.
However Brown knows he may still require surgery on his knee. "You never know and that still might have to happen, but hopefully it won't," said Brown. "It's going pretty well at the moment. I'm running and using the ball and hopefully I can get back in full training soon. It all depends on whether I can go back into training and carry on as normal. I'm a bit wary and I don't reckon I could go back to tackling.
"I could go back and get a knock again and I might then have to have the operation. I'd be scared and it's that sort of thing I have to get over. I just need to start pinging the ball now and do a bit of shooting to get the muscle right."
Brown had hoped to win a regular place at the heart of the United defence and said of his injury: "It's probably the worst thing that can happen for a footballer, but you just have to get on with it.
"Hopefully, if I get fit again, I can get back in the team."