Blues had to play for more than hour with just ten men following the dismissal of Craig Gardner for two bookable offences just 29 minutes into the local derby at St Andrews on Sunday lunchtime.
McLeish admitted to being angry with Gardner's reaction to being fouled by Jamie O'Hara which resulted in referee Kevin Friend branding the Blues midfielder with his first yellow card.
"Craig was silly," McLeish told Sky Sports.
"I told the players not to react to fouls and we had to be mature about this and let the referee deal with it.
"The one that really annoyed me is he put his hands up after O'Hara clattered into him, so that was disappointing.
"I told the players not to react to fouls and we had to be mature about this and let the referee deal with it.
"As soon as you start that stuff, you get a yellow card and put yourself under big pressure.
"I've got to applaud a fantastic result," the Blues boss added.
"There was some grit and, at times, we did quite well with 10 men.
"We had to pick our moments as it was not easy to get forward with numbers, but when we picked our moments we looked really dangerous.
"I am proud of the players and their attitude to go right to the death."