Clark's side went ahead in the 49th minute through on-loan striker Wes Thomas before the persistent Chris Taylor claimed a vital equaliser 20 minutes later.
However Clark did find some praise for his youthful side which has moved out of the relegation area in recent weeks.
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 a Chris Taylor effort into the net. It appeared the goal had been allowed only for the linesman to flag for offside.
Referee Keith Hill seemingly over-ruled this decision but he changed his mind much to the consternation of the Millwall side and the relief of Birmingham.
Commenting on the controversial incident, 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."