That means that the striker will miss Blues' next three league fixtures against Leicester City, Millwall and Leeds United.
The Serb was sent off by referee Andy D'Urso for a challenge on Huddersfield full-back Callum Woods, less than 25 minutes after joining the match as a half-time substitute.
Whilst his foot was slightly high in his attempt to win the ball, there were no studs showing. But having reviewed the incident, the club will not be appealing the decision.
"At the time, from the other side of the pitch, I thought it was harsh," said Blues boss Lee Clark.
"I have seen it since and he's genuinely gone for the ball. He's slid in, seen the lad coming, and has actually tried to pull his leg away when he was sliding, which is very difficult.
"He has caught him, but it wasn't malicious, it was a genuine attempt and I think it was a yellow card probably, not a red."