Clark was forced into fielding a side made up of seven teenage players because of injury problems and suspensions.
Blues took a 30th minute lead against the Clarets courtesy of a Curtis Davies header but the visitors scored twice in three minutes after the break to lead 2-1.
Nikola Zigic salvaged a point for Blues when finding the net in the 89th minute.
"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."