Blues extended their unbeaten run to 12 games with a 1-1 draw against the reigning Premier League Champions at St Andrews on Saturday evening.
Against the run of play, Cameron Jerome netted to give Blues a one-goal lead six minutes before half time but United equalised when the unfortunate Scott Dann put through his own net 18 minutes into the second half.
United also had the misfortune of losing Darren Fletcher for two bookable offences.
"We were fortunate to be leading at half-time but we were a different animal in the second half," McLeish said after the match.
''We knew United have a habit of scoring late goals but when Fletcher went, it possibly gave us a bit more impetus and we could have won it in the end.
''We could have won it in the end, if Cameron could have taken care of a ball. He could have rolled it across the face of goal and wee Chucho would have surely had a tap-in.
''We're not saying we're disappointed, we're playing against a great side - albeit missing a few - but that was another fantastic performance.''