James Milner converted the spot-kick in the 83rd-minute to settle the second City derby at Villa Park and move the home side level on points with fourth-placed Tottenham in the Premier League.
But McLeish was adamant that Johnson had won the ball in the challenge on Villa striker Gabriel Agbonlahor which led to the penalty award and the defender certainly agreed.
The former Cardiff player said: "The decision regarding the penalty was a disgrace. I thought the referee was a disgrace the whole game through if I'm being honest.
"The rules are if you are not sure about a decision, you don't give a penalty and the referee was a million miles away from the incident.
"The linesman could see it better than the referee. But the crowd are getting the sound up and he (the referee) bottled it for me. It is an outrageous decision."
Johnson added: "Did the referee explain the decision? Don't be silly. Referees don't talk to you. They just say 'go away'.
"You can't talk to them. They all ask for respect but you can't talk to them so it is a waste of time."
McLeish, meanwhile, echoed the feelings of Stoke boss Tony Pulis that bigger teams have more decisions going in their favour.
McLeish said: "It was a bad mistake by the referee. It's a shame he gets such a big decision wrong in such a big game.
"I am not questioning his fitness but Agbonlahor, with his pace, is difficult to keep up with.
"The referee was so far behind and he surmised it was a penalty. I have defended referees a lot but I can't defend that one. He got it wrong.
"Roger Johnson has made a name for himself with that kind of tackle. He got the ball cleanly.
"Tony Pulis has said he feels bigger teams get more decisions throughout the course of the season and today was evidence of that."
Villa boss Martin O'Neill had a different perspective on the situation after viewing a slow-motion replay of the incident.
He said: "From the bit I've seen, Johnson has caught Gabby's legs. If he has got the ball first, it becomes a separate issue.
"But from the slow motion, it looks as if he wrapped his legs around Agbonlahor and it was a penalty.
"Referees are now saying it doesn't matter if you touch the ball first. If you are following through with intent, it is a foul.
"If Johnson has got a clean touch on the ball then I will change what I think."
Villa made sure of at least a Europa League spot by defeating their local rivals but O'Neill has his sights higher.
He said: "It has been a great week for us and the consequence of winning today is that we have qualified for Europe.
"We will go into the last two games and give it everything. Manchester City away next week will be exceptionally hard but we will have to try and win."
O'Neill conceded that Birmingham may have deserved something from the game and only a string of fine saves by Brad Friedel kept them in contention before Milner's penalty.
"Birmingham might feel aggrieved because they played very well in the second half," he added.
"Friedel was magnificent. On the second-half performance, they deserved something from the game."
McLeish took consolation from the performance of his players in contrast to the 5-1 defeat in the last Villa Park derby two years ago.
He said: "You tend to think the world is against you when you get a decision like the penalty after playing so well.
"But I am proud of the players. They were magnificent today. Villa edged the first half, but Friedel made three or four great saves."