Blues had managed to contain City' for thirty eight minutes of the game at Eastlands on Sunday afternoon when referee Phil Dowd awarded a dubious penalty to the hosts from which Carlos Tevez gave them a 1-0 lead.
Nedum Onuoha headed home an Adam Johnson's corner to double City's advantage just two minutes later but Blues almost immediately halved the deficit when Cameron Jerome headed home from a James McFadden cross.
However, City quickly restored their two-goal advantage when Craig Bellamy's low cross was slotted home by Emmanuel Adebayor from inside the six-yard box.
The goal which finally killed off Blues' hopes came in the 74th minute when Onuoha played a one-two with Tevez and burst through the defence to score his second and City's fourth with a well-placed shot.
City added a fifth goal in the 88th minute when Adebayor latched onto a clearance from keeper Shay Given and raced clear to slot home a low shot past Maik Taylor in the Blues goal.
"We were solid enough for about 30 minutes," McLeish told Sky Sports after the game.
"We were going well and City were quiet. We'd contained them and then of course the penalty came.
"We thought it was a bit soft but you can see why the referee gave it.
"The second goal was disappointing because we've been good from set pieces but Onuoha got free and it was difficult to keep out.
"We had to chase the game after that and we got a goal back and then unbelievably we lose a soft third goal.
"The two goals in the second half were definitely of the comical variety. At 3-1 we had a couple of chances and we need the next goal.
"There's things to work with, we've got young centre back rookies in the Premier League that have been brilliant this season.
"There's things to work on in terms of the next game, but I see it as a blip today."