Gloucester boss Nigel Davies admitted his team's Amlin Challenge Cup hopes were ended by "a very clinical" Biarritz team at Kingsholm.
Gloucester crashed out after the holders ran in five tries - two from wing Teddy Thomas - to set up an away semi-final against Wasps or Leinster. Biarritz posted three first-half touchdowns while Gloucester had a player in the sin-bin - prop Dario Chistolini and then hooker Koree Britton - and there was no way back from a 13-point interval deficit.
"The first yellow card wasn't a yellow card, simple as that, but that is irrelevant in many ways. More importantly, we couldn't really back up the performance level of last week against Harlequins," said Davies, following Gloucester's 41-31 defeat.
"There was a lot of effort and endeavour, not always directed in the right direction, but that is where this group is at the moment. I thought we played a lot of the rugby out there, but arguably a little too much at times.
"What we saw in Biarritz was a very clinical side. We conceded points just after we scored, and their driving lineout was very strong. Their opportunities came from broken play. We tried to create a lot more than them, but we just lacked the intensity of last week, even though we showed a lot of intent.
"When you have got an ambition to out-play and out-run the opposition, it is very difficult when you go down to 14 men for 20 minutes. That had an effect, there is no doubt about that. It was a strange old game in many ways. We played our part in it, but it was a great experience for this group of players. They will learn a lot from it."
Hooker Arnaud Heguy also touched down for Biarritz, with centre Damien Traille dropping a goal and scrum-half Dimitri Yachvili converting all three touchdowns and booting a penalty for a 27-14 interval advantage.
And with Biarritz's American international wing Takudzwa Ngwenya causing mayhem in broken play, his enterprise delivered a fourth Biarritz try after 57 minutes for centre Benoit Baby that saw Yachvili add the extras, before he converted substitute Seremaia Burotu's late score.
Gloucester had to be content with four Freddie Burns penalties, tries from Mike Tindall, Shane Monahan and Huia Edmonds, plus two Burns conversions, but they were beaten far more convincingly than the 10-point margin suggests.
"We are very happy," said Biarritz's former Gloucester number nine Yachvili. "We knew that Gloucester were playing well in the Premiership, so this is a very good win for us. We are the cup holders, and we know if we win the tournament we will qualify for the Heineken Cup next season. We will keep working hard."