The Blues midfielder was dismissed in the 86th minute of the game at St Andrews for kicking-out out at Bees midfielder Alex Pritchard much to the disappointment of manager Gary Rowett.
“He has let himself down and what has done now is put the team under pressure for the last ten minutes, " Rowett said.
"He has given someone else an opportunity to step into his shoes for three games and make that position his own.
“He is going to suffer more than anyone, he knows that. He is an honest lad, it was just a bit of stupidity.”
Gleeson will now have to sit out Blues' next three games against Blackpool (h). Derby County (a) and Huddersfield (h),