London Wasps' European dreams were ended by a later Dimitri Yachvili penalty at Adams Park but director of rugby Dai Young has praised his side following the defeat after they battled back into contention from 23-9 down.
The visitors were in full control midway through the second period in High Wycombe, leading their hosts by 14 points. But two quick tries from Young's men leveled the scores and set up a dramatic final ten minutes.
It was Biarritz who clinched the victory with Yachvili kicking his side into the semi-finals but Young admitted after the game he was proud his team stuck at the task.
"I thought the players showed a lot of guts and determination to claw themselves back into it and with eight minutes to go it could have gone either way," he said.
"We have to be honest and say that at one stage we were dead and buried. If we had a little more fire-power we could have won it but I am not sure we would have deserved it.
"We were lucky at times but I was very proud of the team, especially the young guys.
"They gave everything and showed a lot of character and they will be better for the experience today.
"There is a disappointed dressing room in there but they should be proud of our run in this competition. We came up against some tough French sides and we gave a good account of ourselves. Today we lacked the fire-power of our opposition and Yachvili was outstanding but we can take the positives and move forward."