Bristol were knocked out of the Challenge Cup after a 33-26 defeat by ASM Clermont Auvergne at Ashton Gate.
Tries from Tomas Lavanini, Damian Penaud and George Moala helped Clermont take the lead as Harry Randall and Semi Radradra scored for Bristol.
Anthony Belleau kicked 13 points to AJ MacGinty's 16, but Penaud doubled his try tally to all but tie up the win.
Clermont progress to the quarter-finals next weekend and will take on Scarlets who beat Brive.
The three-time French winners of the competition started their campaign in the Champions Cup but dropped down to the Challenge Cup after finishing ninth in their pool and having only won one of their group games.
In typical knockout rugby style both teams were nervous and cagey in the opening 20 minutes, with little free-flowing, fluent play.
MacGinty kicked two penalties to one from Belleau, but Clermont's forwards gradually turned the screw. While the American fly-half held up Etienne Fourcade to deny them a try at their first attempt, lock Lavanini then powered over as the French side muscled to the line.
Penaud sprinted in for their second try out of nothing, finding space as Bristol missed the tackle and allowed Clermont to go 11 points clear in five minutes.
The Bears were given an opening back into the match when Clermont captain Fritz Lee was sent to the sin-bin for a high tackle on James Williams.
They pounced instantly through Randall, who darted over from a few metres out, and then Radradra reinstated Bristol's lead after Williams made a break through midfield from inside his own half. The try came at a cost to the Fiji centre, who pulled up on his hamstring and hobbled off straight after scoring.
But again Bristol were punished for mistakes as they knocked the ball on from the restart in a major lapse in concentration, allowing Clermont to gather, pass and score through Moala and go into the break two points up.
Belleau added six more points from penalty kicks either side of another from MacGinty as the French side asserted their dominance in a quiet second half.
Penaud scored his second try after another major Bristol error gifted Clermont the win. The France international chased his own kick and, as Siva Naulago paused as he tried to shepherd the ball out of play, Penaud dived and tapped it down.
Another MacGinty penalty closed the gap to seven points, but it was too late for Bristol to mount a comeback.
Bristol director of rugby Pat Lam told BBC Radio Bristol:
"I'm frustrated, obviously. We talked before the game about the conditions and everything, this is all about playing at the right end - whoever plays down the right end will get it.
"We did some really good things down this end but we coughed up the ball too easily at times.
"We talked about it at half-time but even before half-time we scored and took the lead, we got up from our seats and went down ready to talk about it and then I heard a crowd noise and said, 'Have we scored again?' and they said, 'No, they scored.' I didn't see what happened, I found out what happened.
"We spoke about how we've got to start the second half well and come back in it, but we gave away another soft try.
"What I was proud of is we got back within a try and the boys tried to give it a go at the end. I'm proud of the effort at the end but we've got only ourselves to blame with the soft tries we conceded."
Bristol: Piutau, Naulago, Radradra, Williams, Ibitoye, MacGinty, Randall; Genge, Thacker, Sinckler, Bradbury, Vui, Luatua, Jeffries, Harding.
Replacements: Capon, Y Thomas, Kloska, Rice, Heenan, Uren, Bedlow, Lloyd.
Clermont: Newsome, Penaud, Simone, Moala, Delguy, Belleau, Bezy; Falgoux, Fourcade, Ojovan, Lanen, Lavanini, Tixeront, Dessaigne, Lee.
Replacements: Jules-Rosette, Beria, Slimani, Annandale, Godener, Jauneau, Plisson, Raka.
Sin-bin: Lee (31).
Referee: Jaco Peyper