The Lions created a host of good chances, while top scorer Steve Morison missed a penalty, but they only had Danny Schofield's late consolation to show for their efforts.
Birmingham, by contrast, finished like a Premier League team with Matt Derbyshire scoring twice and David Murphy and Cameron Jerome also on target.
"We needed the first goal but we didn't get it," shrugged Jackett.
"Birmingham were clinical but they were poor goals to give away.
"Saying that, we had a lot of chances and played well. There were lessons learned."
Source: PA
Source: PA