Despite going down 19-11 to Stade Francais Paris at the Stade Jean Boin on Friday Bristol skipper Matt Salter thinks his side can make it into the quarter-finals.
Bristol have 13 points, three behind Pool leaders Cardiff Blues, and have a showdown with the Welsh side next Sunday.
"It's an even pool and we're still in the mix," he said after the eight point loss in Paris.
But to leave France without even a losing bonus point means Bristol have to win next week or face elimination.
Trailing by just three points at the break, Bristol came out in the second half feeling the match was well within their grasp.
"We fancied it in the second half and felt going in against the wind only 9-6 behind," said Salter.
"It was all there for us and we felt we could do it but they pinned us back well into our 22.
"We are genuinely gutted because there was a big chance for us to win here,"
.