Exeter crashed to a 40-17 defeat to Bayonne in their Investec Champions Cup clash in France.
The Chiefs, already assured of a home tie in the last 16, were punished for their indiscipline as the hosts, who sit fifth in Pool C, ran in six tries.
The defeat means Exeter will take on Gallagher Premiership rivals Bath in the next round.
The French side scored first as outside centre Sireli Maqala sliced through Exeter’s defence with some neat footwork before finding Tom Spring, who showed great pace to score. Thomas Dolhagaray converted to make it 7-0.
Exeter responded through Dan Frost and reliable kicker Henry Slade added the extras to level the score at 7-7.
But Bayonne bounced back after a mistake from Exeter’s Josh Hodge. The full-back failed to control the loose ball and Kote Mikautadze went over.
After Exeter’s Ollie Devoto was shown a yellow card, Bayonne took advantage through Aurelien Callandret, who crossed to make it 19-7.
Bayonne added the bonus point through Victor Hannoun, but the Chiefs scored two quick tries in the second half through Dafydd Jenkins and Rusi Tuima which helped the English side narrow the deficit to 26-17.
Despite Callandret picking up a yellow card for an intentional knock-on, Bayonne’s resolute defence withstood Exeter’s attacking pressure and they managed to score a try of their own through Federico Mori in the 65th minute, making it 33-17.
Yellow cards for Jenkins and Jack Yeandle, either side of Mori’s second try of the game, ended Exeter’s hopes and they lost another player in the closing stages as Joe Hawkins was shown a straight red for a head-on-head collision.