Nikola Zigic handed Blues an early lead but they were then pegged back by first-half goals from Marcos Alonso and Chung-Yong Lee, prior to a late Keith Andrews penalty wrapping up victory for the Trotters.
Reflecting on the disappointing result, Clark said: “We made a good start – and then it all went wrong.
“I wasn’t happy with our performance at all after we took the lead. I thought that was our most inept performance for many weeks. I’m furious.”
Trying to put his finger on where it went wrong, Clark continued: “It’s because we allowed what we talked about to happen. We allowed (Jay) Spearing and Andrews to dictate the tempo of the game and to be unopposed every time they received the ball.
“We said one of their strengths is their passing ability and they kept feeding their wide men (Chris) Eagles and Yong-Lee so we gave ourselves problems.”
Zigic added to the shortage of striking options by seeing red for two bookable offences, leaving Clark with a major selection headache at home to Cardiff City on New Year’s Day (3pm kick-off).
The Blues boss added: “It’s left us with zero strikers for New Year’s Day in terms of experienced strikers. All of young Jake Jervis’ football has come during loan moves so he’s come on for ten minutes today.
“I’m disappointed with Nikola because he’s been a terrific example; a good leader; a good experienced player; he’s got vital goals; he’s been strong for the team and been a good example to the youngsters.
“But he’s let his frustrations get the better of him today and obviously we’ll lose him against the league leaders, which leaves us with one hell of a conundrum to come up with.”