The game was settled as a result of a mistake by Blues goalkeeper, Jack Butland, who might have made his last appearance as he could be released in a fire-sale to produce some much-needed finance for the Midlands club.
An optimistic long-range shot by Craig Conway appeared to be going wide of the post in the 41st minute when Butland decided to parry the ball.
Unfortunately for the young England goalkeeper he only pushed the ball out to Joe Mason to fire into an empty net for Cardiff's 18th win of the season.
It was a terrible setback for a young Birmingham side in which Nathan Redmond, Ravel Morrison and Rob Hall produced some attractive attacking football.
Clark said: "Without a doubt we deserved something from the game. The goal we gave away was very unfortunate.
"Butland saves the shot but then the ball hit him on the back of the head and then on the back of the heel and rolls straight to Joe Mason to tap it in.
"We played some excellent football. It is horrible because we are in a business where picking up points is vitally important but all the performances collectively were very good against a team which is going to get promoted."