Blues progressed to the last 16 of the competition the hard way having been 2-0 down to the Sky Blues with just 26 minutes of the cup tie played.
However, David Bentley reduced the deficit before half-time with a stunning strike from 25 yards for his first Blues goal and, after a sustained spell of pressure, two goals in six minutes from Stuart Parnaby and Kevin Phillips midway through the second half completed the turnaround.
"I wouldn't want to live through that too often with the stress levels but I thought the team played well today. There was a lot of really good stuff," the Blues boss told Sky Sports after the game at St Andrews.
"We shouldn't have made it hard for ourselves because we started great. Coventry are obviously very dangerous up front.
"The big lad Clive Platt was a handful and of course we all know about Marlon King. But I knew there were goals in it for us.
"Bentley's was a cracker. We needed that. It was a turning point. If we'd gone in 2-0 down it would have been much tougher.
"The second half was again a measure of this squad's resilience and their desire not to give up until the final whistle."