Liverpool came close to overturning a three-goal deficit for the first time since entering Continental competition 32 years ago in their semi- final, second leg at Anfield but fell a goal short.
After goals from Robbie Fowler and Mark Wright had given the holders the fright of their lives, Bjornebye dedicated Liverpool's show of defiance to those who have branded them a bunch of fancy dans lacking the heart to match the best whenever the going gets tough.
"We are very disappointed to have gone out because we feel that over the two games we were good enough to go to Rotterdam to play Barcelona in the final," he said. "But there's also a sense of relief as well because we got some pride back after that performance.
"We've had some disappointing results lately, losing to Coventry, getting beat in Paris and then playing poorly against Manchester United but we showed that the criticism we've had for a lack or pride or a lack of heart or whatever people want to call it is rubbish.
"We showed those people that we are prepared to die for the club and in the end we are very unlucky to be going out of the competition."
When Fowler scored his 31st goal of the campaign, and his seventh in Europe, in what was his last club game of the season with a three-match ban about to start, Liverpool were rampant and looking well capable of avenging their 3-0 surrender in the Parc des Princes two weeks ago.
However, despite battering Paris they had to wait until 11 minutes from time before Wright headed the second goal from Bjornebye's corner.
"We needed an early goal and we got it," the Norwegian said. "When we got the second one with 10 or so minutes left I thought we were going to do it and if we had managed to take the game into extra time then we would have been cruising.
"There's no doubt that Paris were afraid of us and they were lucky to get away with it because we had a few chances to get the third goal as well.
"We lost the game but we should be happy about the other things we showed. We showed our pride and played some good football. It was a quality performance."
Liverpool have three games to show that this is no false dawn after seeing their Premiership title dream disappear after Manchester United's 3-1 Anfield win last Saturday.
Nine points would bring the runners-up spot and the European Cup place that now goes with it.
"It's important that we carry that on by getting the results we need in our last three games to claim that second European Cup place," Bjornebye said. "That would be a nice reward for us. We've been a bit inconsistent but no one should forget the fact that we have also played some great football and we've learned a lot from playing in Europe."Reuse content