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Williams was the Parisian hero on the night, claiming the match-winning try with just over a minute on the clock after Exeter had looked set to take the hosts to extra time.
Having been replaced by Jerome Fillol in the dying stages in the French capital, Contepomi was forced to look on from the bench as time ebbed away before his Samoan team-mate saved the day by surging over to the right of the sticks.
"It was so stressful to spend the last few minutes of the game on the bench," said Contepomi, who was watching from the sidelines for the second time in the match having been sinbinned for striking Exeter hooker Chris Whitehead in the 25th minute.
"Exeter came here with a lot of ambition and they played very well and gave us a really good game.
"It's always the same with the English teams: matches against them are always very, very tough. They are maybe a little bit predictable but they are always of a very high level, especially in terms of the fight and the intensity that they bring.
"But we answered the questions they asked of us and gained what is a crucial win for the club.
"Maybe we don't have a huge squad this year but every single one of my team-mates has my full confidence. We are united and that is our strength."
As for who Stade wish to face in the semi-finals, Williams isn't fussed. The former Sale Shark knows both Toulon and Harlequins will provide stiff opposition but he insists Stade are just thankful to be in with a shot at a first European trophy having come so, so close last time out.
"Both those teams would be a great challenge for our team and with that challenge comes excitement," said Williams.
"I know Harlequins are having a great year and Toulon are also doing well here in France, so how do you choose? Either way it will be a great occasion and one that we'll look forward to.
"There was a fair amount of relief after the Exeter game. Exeter are having a fantastic season and they played well again against us.
"We feel like we made a lot of tackles and were chasing them around so we're pretty relived to have made it through."
