Despite the fact television showed Dimitar Berbatov's two goals giving the European champions an irretrievable advantage and an immeasurable increase in confidence both to be offside, the Parkhead manager preferred to regard United as "the best European team of my time as a manager".
Strachan might almost have been obliquely protecting his own players from excessive criticism as he lauded Sir Alex Ferguson's side after a match that has left the Scottish champions' prospects of qualifying for the last 16 of Europe's premier tournament for a third successive year virtually eradicated. Having drawn at home to Aalborg in their opening match and lost to Villarreal in Spain in their second, Celtic have taken just one point at the half-way stage of the campaign.
The manager conceded the near-certainty of failure to qualify when he said: "I think realistically we are looking at third in the group and a place in the Uefa Cup." The return with United is at Celtic Park is due in two weeks' time and it seemed obvious that even the tigerishly competitive Strachan does not harbour serious expectation of repeating the 1-0 victory in the same fixture two years ago.
"Listen," he said, when the subject of the return was raised, "don't even go there. I'm still seeing a red tide in front of my eyes and can't even think about two weeks from now. It's a night for getting on the bus for home, having a cup of tea and going to sleep."
During his praise of the winners, Strachan described the England striker, Wayne Rooney scorer of the third goal as "unplayable" when at the top of his form. "When you see something like that," said Strachan, "you just admit that you've just seen a world-class player, backed up by one or two other world-class players and another eight great players.
"I said to our players at the beginning of the game that we can't be faulted for our guts and determination. Where we do fall down is that we aren't anywhere near them (United] in terms of passing the ball and movement.
"We couldn't match them physically and so we had to try something else. And we didn't start that well in the sense of keeping possession.
"But, having seemed to settle after that and really keeping their opportunities very limited, we go and lose a goal from a set piece. I know the first two goals were offside I'm told that by the TV people but I'm not going to scream about them. I'm a football man and I know when I'm beaten, in fact well beaten.
"I know we needed a break and didn't get one tonight, but United gave one of the best performances I've seen in Europe in my time.