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."
Source: PA
Source: PA