And while disappointed with the result, Leicester coach Burke was pleased that the Tigers managed to pick something up on the road thanks to a late penalty from Owen Williams.
"It's disappointing to lose but the guys showed a great attitude to get something out of the game when it could have got away from us. At nine points down they were getting pressure on us and you can't afford to let them out of reach," said Burke.
"We had a lot of players missing - 10 in the backs - but the guys who are in the dressing room take a huge amount of pride in pulling on the jersey and defending their line when they have to.
"The attitude to dig in for each other and to put bodies on the line was outstanding, especially in the spell when we were down to 14 men. It shows the character of the team and the point in the end was testament to that determination and that attitude."
Logovii Mulipola handed the Tigers an early lead at Ravenhill but the hosts clawed their way back. Tommy Bowe leaped for a sensational try, his 24th in the tournament and one short of an ERC Elite Award, and Jackson edged his kicking dual with Toby Flood.
"We got off to a very good start and controlled the ball well to create the chance for the try from Logo," added Burke. "To come back and keep enough composure to keep going and to get back at the death showed some real quality and strength of character.
"That's a really good penalty from Owen Williams in his Heineken Cup debut for us, they're the hard ones when the pressure is on. We targeted a strong start because we knew they would come hard at us and knew the crowd would be vocal as it always is at Ravenhill.
"It's a difficult place to come and, though we wanted the win, taking something out of the game is important. We've learned from past years that if you don't take anything from your away games then that can come back and bite you in the later rounds."
The Tigers take on Benetton Treviso at Welford Road in Round Two.