Curtis Davies opened the scoring for the youthful hosts, but Burnley hit back with goals from Danny Ings and Ross Wallace before Nikola Zigic's late strike snatched a point for Birmingham.
The Blues had fought back to claim a point against Crystal Palace the previous weekend and Clark was delighted with their never-say-die attitude.
"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."