Clark had seven teenagers in his side and things looked promising after Curtis Davies scored in the first half for only his second goal of the season.
Burnley fought back with two goals in the space of two minutes from Danny Ings and Ross Wallace, but Birmingham struck late to salvage a point.
"It was another comeback," Clark said. "We deserved the draw with the youngsters putting up a spirited performance.
"That was our best first half at home for many games. There were a couple of situations Burnley had in the early part of the game. But we dealt with that and we deservedly took the lead.
"Then there was a mad couple of minutes in the second half when Burnley scored twice.
"Burnley had a spell for 25 minutes but we switched from doing the basic things.
"To give away the ball from the restart gave them an opportunity because we were fully aware that Ross Wallace has a terrific delivery and I don't think many goalkeepers would have stopped that free-kick."
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- Ross Wallace