Bowyer retaliated after being on the receiving end of a challenge from Baggies defender Gonzalo Jara and reacted with a lunge at Gabriel Tamas which resulted in him picking up a yellow card.
McLeish instantly substituted Bowyer, who was then involved in a verbal exchange with a female fan situated behind the City dugout.
McLeish said: "I just didn't want to take a chance. Lee is mature but I didn't want to take a chance and get egg on my face.
"We were talking about taking Alexander Hleb off at that time because he has not played a lot of football and he looked fatigued.
"Then Bowyer got the booking and I took him off just in case. He is more mature now and he maybe would have seen it through but I didn't want to take any chances."
As regards the Bowyer-fan confrontation, McLeish said: "Someone lambasted Lee when he came off and I saw 'Bow' trying to pacify them.
"That's the only thing I can tell you about it. I know some people were having a go from the seats behind the dugout. When I turned around 'Bow' was telling them to calm down.
"It is difficult when you are coming off the pitch, have been booked, been taken off when you don't want to come off, and someone is lambasting you from the terracing."
McLeish admitted his side paid for some sloppy mistakes as Albion recovered from a 1-0 half-time deficit.
He said: "I am stunned by the mistakes we made, human errors.
"I've been telling you every week about the character in this team. Today that wasn't evident in the second half, unlike us.
"West Brom changed their shape which I thought they might do but it was very unlike us to capitulate.
"The mistakes gave them a way back into it, nothing to do with systems, and after that we were never really at the races.
"It was very untypical of this team. We said that in the dressing room and some of the players admitted that as well."
Baggies boss Roberto Di Matteo replaced striker Marc-Antoine Fortune with midfielder Graham Dorrans at half-time and pushed Peter Odemwingie further forward - a move which paid dividends.
He said: "The aim was to get a win and we did it and it was a good performance.
"We controlled the majority of the game and managed to score three goals in the second half.
"It was a bit disappointing the goal we conceded from a set piece -
but apart from that we didn't give them any chances.
"We didn't get hold of midfield in the first half. It is a bit of a risky move because you are 1-0 down and we removed a striker.
"But I felt I had to get another midfielder on but I put Peter up front and it worked.
"It doesn't always come off. It's the players who have to perform and they did brilliantly in the second half.
"Peter was a threat, a good outlet, but it was not just him. The whole team stepped it up in the second half."