Tigers trailed by 10 points entering the last 10 minutes of the game before a Toby Flood penalty and a converted try from Ed Slater earned a share of the points in the Round 5 clash in front of a capacity 24,000 crowd.
Backs coach Burke said: “It wasn’t a great game from our point of view for the first 65 or 70 minutes. We played too deep at times and against a quality side like Northampton we tried to force it a bit. We had the upper hand in the set-piece and that should have allowed us to get some good position and get a squeeze on them, but we couldn’t do that.
“Credit, though, to the guys because the last 15 minutes were amazing. We got back into the game and we still could have nicked it with that scrum at the end. It was an outstanding effort to come back when it looked dead and buried.”
Saints led 9-6 at half-time and claimed the opening try of the second half through prop Alex Corbisiero as they stretched their advantage.
Tigers went close on a couple of occasions before Slater finally found a breakthrough score and had the crowd on the edge of their seats for the closing moments.
“We had our opportunities but our error count was too high,” said Burke.
“We spoke about it straight after the game. We have to look at that as a group because our error count over the last three or four games has been too high.
“You have to be able to maintain pressure on teams, to keep field position and not cough up ball.
“We were there or thereabouts in the last few minutes but the first 60 minutes by our standards were not good enough.
“Then, just when the game looked like it was pulling away from us, we started to play in the right areas, carry ball and recycle, and execute everything we talked about before the game and again at half-time.”
Tigers remain in third place in the Aviva Premiership table after the opening five rounds of the season’s action. Now they go to Ulster on Friday in the first game in the pool stages of Europe’s Heineken Cup.