France's hopes for the Six Nations were dealt a huge blow towards the end of the first half here, when Clermont's centre, Wesley Fofana, a key member of Les Bleus' midfield, ruptured his Achilles tendon. He will now miss the entire championship.
In a statement on their website, Clermont said the 29-year-old would need an operation on his left leg.
In the game itself, Exeter's hopes of a Champions Cup quarter-final were ended by a ruthless first-half display from Clermont Auvergne, who bagged five tries to lead 34-0 at the break.
The Chiefs had to play the latter stages of the half with only 13 men after losing Olly Woodburn and Ollie Devoto to controversial yellow cards in the space of only two minutes.
However, they showed guts and determination to grab four tries after the interval to claim a positive or two to take back to Devon.
Exeter head coach Rob Baxter was annoyed by the sin-binnings of Woodburn - for a deliberate knock-on that resulted in a penalty try - and Devoto for a high tackle on Nick Abendanon, as the decisions by Irish referee Andrew Brace cost his side 19 points.
"From what we could pick up, it seemed like the referee was determined to yellow-card Olly Woodburn, despite people saying he had knocked the ball backwards and he was pushed as well as he tried to get hold of the ball," said Baxter. "There were so many reasons you could find to not make that a penalty try and a yellow card.
"As for Ollie Devoto, I cannot believe World Rugby want that to be a yellow card. We are talking about contact that was only a foot off the ground. But if I am honest, we would not have been in those scenarios, if we had shown more intensity. I am pretty disappointed with our performance overall.
"You have got to do your job flat out, and that is what we have focused on. It has been the driving force behind our upsurge in form, about individual players taking responsibility for their parts in the game, and it is hard to say that was happening out there today.
"Clermont are a very good side, but we didn't have too many issues knocking over and tackling international-quality players against Ulster last week, but in the first 30 minutes today, it looked like we hardly made a tackle."
Chiefs needed to win and hope other results went their way to stand any chance of reaching the last eight, but their chances were all but over inside nine minutes, in which tries by Benjamin Kayser and Noa Nakaitaci and a conversion and a penalty by Morgan Parra put Clermont 15-0 up.