Old Trafford boss Alex Ferguson was in the stand at Fir Park to watch Rangers held to a draw by Motherwell in a game that both sides had chances to win.
The result was not the ideal preparation McLeish was seeking ahead of Wednesday night's Champions League showdown and he knows that his former mentor, Ferguson, will have left Motherwell confident that his own side's European campaign will be back on track at Ibrox.
McLeish admits his players played nowhere near their full potential against Terry Butcher's men and he has told them they must improve before Roy Keane et al come calling.
"I think Sir Alex will be thinking that, if Rangers play like that today, that Manchester United will win comfortably. But we have a lot more in the team than we showed today and the players know they have to raise their game on Wednesday night.
"That will be a different game and, at the end of the day, we know what we are facing. We are not the bookies' favourites we realise that and we need to do a bit of work between now and Wednesday to make sure that we do a whole lot better."
McLeish denied that his players' minds were already on the clash with Manchester United and that led to them dropping vital league points.
Shota Arveladze opened the scoring for Rangers but that was soon cancelled out by Stephen Pearson and the points could have gone either way after that.
The 1-1 draw means that Celtic have increased their lead at the top of the Bank of Scotland Premier League table to three points this weekend, but McLeish admits Rangers cannot take it for granted they will defeat non-Old Firm opposition.
Motherwell boss Butcher claimed yesterday's result will not necessarily have an impact on Rangers' meeting with United. And he believes their performance against the Ibrox side shows that it is possible for underdogs to triumph with the backing of their own supporters.
He said: "Playing league games and playing in the Champions League are totally different games but I'm sure Alex McLeish is hoping Wednesday's game won't be as open as today.
MOTHERWELL: Marshall, Corrigan, Craigan, Partridge, Hammell, Lasley, Adams, Leitch, Pearson, Craig (Dair 79), Clarkson.
RANGERS: Klos, Berg, Khizanishvili, Moore, Ricksen (Capucho 79), Arteta, Emerson (Vanoli 66), Ball, Lovenkrands (Ostenstad 69), Arveladze, Mols.
Referee: D McDonald (Scotland).