Having twice won Europe's premier prize as a player in 2001 and 2002, Cockerill would love to have added a third crown as a coach but a 70th-minute penalty from Jonathan Sexton saw Leinster secure a 19-16 victory at Murrayfield.
"I'm very proud of the performance," said Cockerill, who took the head coach's role at Leicester after previous incumbent Heyneke Meyer returned to South Africa for family reasons mid-way through the season.
"You could not have asked any more from the team out there. They worked as hard as they could work. Sure, they weren't perfect at times but I won't have it that we weren't up for the game. We couldn't have given any more."
Despite falling just short in Europe's showpiece event, Cockerill was keen to emphasise the achievements of his entire squad throughout what has been a hugely successful season.
A total of 12 wins in their last 13 games leading up to yesterday's final saw the Tigers claim the Guinness Premiership title and come so close to their third Heineken Cup crown.
Cockerill admitted that the pain of defeat would linger but that his side should take a great deal pride in their recent achievements.
"We worked very hard, they gave everything and we should be very pleased and proud of our season," added Cockerill.
"We're English Champions and we've lost by three points in the Heineken Cup Final. It could have gone either way but Leinster have to take the credit because they won it. I've got no complaints with that. I'm not going to moan or make an excuse because that's not the way we do things here.
"We're disappointed that we lost obviously. I'm not a great loser but you have to be dignified and that's us. We weren't as accurate as we would have liked; our lineout fell apart at times; we had chances early in that second half to score and we didn't take them, and they came back at us because they're a good side.
"We've had four massive games recently. We could have lost last week and we could have lost in the semi-final of this competition. We've had our bit of luck and maybe our luck ran out. Maybe we didn't quite have the breaks that we'd have liked, maybe we didn't deserve the breaks because we didn't earn them.
"The boys have been manful all year. Our run has been the best of any domestic team in Europe since after Christmas. We came up short. Not by much but it's all about small margins in big games."