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Cheika's charges matched the physical approach of their English opponents despite a taxing Top 14 defeat to Toulouse last weekend and the Australian was full of praise for their attitude as they booked a final four meeting with either Harlequins or Toulon.
"I think that we wanted it more in the end because they had plenty of ball," said Cheika, after a 79th minute try from Samoan centre Paul Williams prevented the first game of a bumper weekend of European rugby from heading into extra time.
"We said at half-time that this one was going down to the 80 and it certainly did. For us to back up from the match against Toulouse, which was a huge disappointment for us, was really a great effort by the team.
"It was a good old-fashioned shin dig. They were bashing us and we were bashing them back. There were a few fights, lots of hard tackles and plenty of aggression. That's Europe and it was great - teams don't know each other and they just jump in and get stuck in.
"I was really happy at half time because they came fully loaded and smashed us in a lot of areas but we got up off the floor and kept coming back. We knew that, if we just kept getting stuck in there, eventually it would come because we've got some class players."
Whoever Stade face in the semi-finals, there is sure to be some added spice as both match ups have a historical context that doesn't favour the Parisians.
Stade's hopes of Heineken Cup qualification and Amlin Challenge Cup glory were ended by Quins in the dying moment's of last year's final in Cardiff, while Toulon have had the upper hand in their domestic battles so far this term.
And while Cheika insists he won't be losing any sleep over who will win tomorrow's second quarter-final, the man who led Leinster to Heineken Cup success in 2009 is certainly looking forward to a massive challenge.
"I don't mind who we play. As long as we're there, that's what matters," added Cheika.
"There's a few weeks between now and the semi-final but both of those teams mean something for us, obviously.
"We were very disappointed to lose to Harlequins in the final last year and Toulon gave us a good spanking down at their place and then snatched a draw at the Stade de France so we'd be keen to play them as well.
"We just want to enjoy the last four or five weeks of our season and try and make the finals of both our competitions."
