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Four unanswered tries in the last hour saw Stade home, with the Parisian giants displaying their fighting qualities to keep their hopes of a first-ever continental trophy alive.
"It was a tough win because we played very badly in the first half," said Parisse.
"The first 20 minutes were a disaster. We were losing 16-0 so it was very difficult to come back.
"But the guys knew that it would be possible for us to change the score in the second half and the second half was much better.
"We were really disappointed with the level of rugby we showed but the victory was most important for us to be able to play the semi-final.
"We didn't play a good match but it was great for the team to come back, score a couple of tries and win - that was the most important thing."
After a shocking start in the French capital, Stade turned on the style at various stages of an entertaining encounter, with England Sevens wing Ollie Phillips and Scotland full back Hugo Southwell in particular producing moments of magic.
When the home side kept possession and went through more than a few phases, they always looked like scoring, but little errors such as forward passes, dropped balls or unrealistic offloads halted their progress.
And Parisse, one of the most talented ball-playing back rows in world rugby, admits his side will need to step up a couple of gears if they are to power past French Champions Clermont in three weeks time.
"We played some good rugby but sometimes we threw 50/50 passes and dropped a lot of balls," added Parisse.
"We had a scare towards the final whistle because they were so close to getting a score. I was really happy for the team in the last play because we produced a really good scrum and that finished the match.
"We showed that we can play very good rugby and score tries, but against stronger teams than Montpellier, like Clermont, we can't give them a head start in the first half and then try to come back in the second. Against Clermont, or then Munster or Harlequins, it will be very difficult if we do that.
"There's still a long way to the final. We face Clermont in the semi final and that won't be easy for us. We have two matches to win the final and that would be amazing for us, for the team and for the Club.
"But we must focus on the match against Clermont because we can't play like we did against Montpellier."
