Alan Pardew's side were 2-0 winners at St Andrews on Tuesday evening thanks to goals from Peter Lovenkrands and Leon Best.
The Blues boss admitted that his side lacked inspiration and looked weary after a five game unbeaten run in League and Cup competitions over the past month.
"We've had a fantastic month really in terms of results since the game against Manchester United at Old Trafford," he told BBC Radio after the match.
"There have been some inspired performances but tonight we looked a bit flat.
"To lose the first goal so easily as we did and so early goes against what we were like at the weekend against Stoke when the concentration levels were phenomenal.
"I think there was a bit of fatigue. One or two players looked a bit tired and I am not going to hammer the players after one performance like that."