Clark's first return to the John Smith's Stadium since his dismissal last year looked to be ending in the best possible way after Academy graduate Callum Reilly fired his side in front in first-half stoppage time.
But Huddersfield's on-loan midfielder Adam Hammill came off the bench to curl into the top corner.
"I am gutted about the result. The key for us is to kill teams off," said Clark. "When the opposition are only one goal down then they have always got a chance.
"When you are 40 seconds away from the end and you concede an equaliser it is a kick in the guts and we have to bounce back.
"Callum was ill during the week, but put himself forward to play. He has scored his first goal for the club and should be immensely proud of himself. I am excited by how we have played in the last seven or eight games, with the exception of Bolton.
"We are playing a brand of high-tempo passing football that I like to play. If we keep playing like that then we will get the rub of the green."
Birmingham continued to put the Terriers under pressure after going ahead through Reilly. Chris Burke nearly doubled the visitors' lead when he curled a powerful shot wide on the hour mark.
But the Terriers, who are now without a Championship win in their last 11 outings, came back strongly in the closing stages with Alan Lee and Jermaine Beckford both coming close to equalising.
Hammill then escaped three defenders before firing a curling shot into the top corner from just inside the box to level in the 93rd minute.
- Sports & Recreation
- Adam Hammill