“A lot of the targets we set ourselves this week we achieved in the first 10 to 15 minutes.”

The hosts had Ma’ama Vaipulu sent off for a high tackle on Luke Cowan-Dickie shortly before half-time, but Exeter failed to capitalise on their numerical advantage.

In the end, a yellow card for Henry Slade for tripping Viallelle in a race to the line seven minutes from time cut short any hope of an Exeter comeback.

Baxter said: “It was pretty tough, especially playing the second half against 14 men, to get outfought through that second half. You have to give Castres great credit for that.”

However, he refused to throw in the towel after two matches which have brought a draw at home to Munster and this weekend’s loss in southwest France.

“It’s a funny scenario,” he said. “If we’d come through two games with four points that’s par, and people can deal with that in the first two rounds. We’re a point behind that schedule.

“If we win our next two, it pulls it back alive. But this is it. There are no more second chances.”

Baxter was particularly frustrated at Exeter’s inability to make the most of their fast start, and said: “You could almost tell Castres hadn’t really had any part of the game.

“We caught them a little bit unawares but literally with their first attack they damaged us.

“Once we’d got those 14 points, if we could have just locked ourselves down with 10 or 15 minutes of solid defence and good discipline we could have made today count. But although we scored well, and we scored quickly, we also conceded quickly.”

Castres’ defence coach Joe El-Abd praised the character of his players after their impressive fightback.

“We know that Exeter keep hold of the ball and they put us under a lot of pressure,” he said. “But at 14-0 down I think we saw the character of the guys to come back into it. And with the red card and everything it was an unbelievable performance.”

Like Baxter, he predicted the next block of games will be vital for Castres’ chances of qualifying from the tightest of pools.

El-Abd said: “We have a double header with Munster next. We need to put in performances like today if we want to progress.

“We got a point at Gloucester. Exeter got a point today. It’s a pool that’s really close, we need a win away from home. It’s going to be very difficult at either Munster or Exeter away.

“Culturally the Champions Cup hasn’t always been the number one focus in France. There are some teams that attack it, others don’t. In the past Castres haven’t, but now we want to go for it.”

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