The Blues went ahead in the 49th minute through on-loan striker Wes Thomas before the persistent Chris Taylor to claim a vital equaliser 20 minutes later.
He said: "They are doing really great and we are proud of them but we have got to be more ruthless and more professional. At times you could see we were young and naive. Their power and physicality brushed us aside at times."
The major talking point occurred in the 20th minute when Richard Chaplow turned in a Taylor cross, only for the linesman to rule it out for offside.
Referee Keith Hill, seemingly over-ruled the decision but changed his mind again much to the relief of Birmingham.
Commenting upon the first-half incident involving referee Hill, Clark said: "I was right next to the fourth official and within a second of the incident he was on the ear-piece telling the referee it wasn't a goal.
"For some reason he didn't hear and went across to his colleague who didn't think the Millwall player hadn't touched the ball.
"He clearly had and being in an offside position it had not to be given. The frustrating thing for Kenny Jackett when he watches it is his lad didn't have to touch the ball as it was going into the net.
"It was the right decision and the officials worked well as a team and prevented a controversial goal being given."