But it was Burke who again engineered Birmingham's late equaliser with an accurate corner which Kyle Bartley headed home four minutes into injury time - just four minutes after coming on as a late substitute.
Middlesbrough, who had only once in their previous 15 visits to St Andrew's desperately need to find some winning away form.
Their failure to beat Birmingham means they have only won once in 23 games on their travels and picked up just seven points.
Spaniard Karanka said: "We were playing and working very well only to lose everything in the last minute.
"We need to improve in this period of the match and not to concede such vital goals.
"We are only four points above the relegation zone and not in a very comfortable position.
"When I arrived the most important thing is getting the points as it makes the players and myself more confident.
"It is not the first time it has occurred - but we have made mistakes late in the game.
"This is the second time in a few days that we have lost vital points. We know it is a probable and we were aware before the game that Birmingham are very good at set-pieces.
"At half-time I told my players that we needed a second goal to win the game but Birmingham played very well in the second half to score two goals and earn a draw."