Tigers were unable to add the European crown to their domestic title after losing 19-16 to Leinster at Murrayfield.
Head coach Cockerill said his players could not have given any more in Saturday’s final and can be proud of their achievements this season.
Cockerill said: “We are disappointed to lose. It was a tight game, it was three points the difference.
“We couldn’t have given any more. The boys played their hearts out.
“I am very proud of the performance. You couldn’t ask for any more from the team out there. They worked as hard as they could work and gave everything.
“We should be very pleased and proud of our season. We are English champions and we have lost by three points in the Heineken Cup Final, and it could have gone either way.
“You have to give Leinster credit because they stuck in the game and they fought hard too.
“The boys have been manful the whole year. Our run has been the best of any team in Europe from after Christmas. We should take a lot of credit for the way we have played this year.”