Blues, like in most of their matches this season, dominated the majority of play but just lacked that clinical edge.
Goalkeeper Zach Jeacock was called into action early on into the first-half after making an acrobatic save to deny a Burnley attacker from close range.
Despite having the bulk of possession in the opening stages, Blues fell behind due to a miscommunication at the back.
Jeacock committed himself on the right only to lose out and the ball was floated across goal for a Burnley forward to stroke the ball into an empty net.
The visitors doubled the advantage moments later through an own goal. A free-kick from the left-hand side was met by Kane Thompson-Sommers and it trickled into the far corner.
Blues went into the break frustrated having seen a lot of the ball but unable to breakdown a resolute Burnley defence.
This carried on into the second-half. The organisation and shape of Burnley’s defence halted Blues from making a breakthrough on goal.
Just before the hour mark, the visitors added insult to injury by scoring their third through a counter-attack. An effort from the right-hand side managed to creep in past Jeacock at his near post.
Even at 3-0 down, Blues still piled on the pressure - the had 73 per cent possession all told in this PDL match.
Forward Adan George had a great chance to pull one back but his close-range effort was matched by the Burnley goalkeeper, who parried away for a corner.
However, Blues did manage to get on the scoresheet, via full-back Lucas Powell. The defender picked up the ball and made a darting run into the box and fired his shot into the far corner.
Blues continued to press on, but Burnley seemed to tighten their defence by throwing a few midfielders back to ensure their victory.
Steve Spooner’s side were unfortunate having dominated the majority of proceedings. A huge test to regain that winning momentum lies ahead as they face Sheffield United at home on Saturday.
Blues: Jeacock, Powell, Moore, Campbell, Kinina, Walker (Mitchell 83), Mayuba (Ajose 60) , Bellingham, Thompson-Sommers, George, Traore. Subs not used: Clayton, Williams, Noakes, Knight.