And while Stade may not have been at their best for the full 80 minutes, Cheika was keen for his troops to celebrate reaching a European semi-final.
"The players came in the dressing room and they were upset," said Cheika, who led Leinster to Heineken Cup glory in 2009.
"I said to them, 'sometimes you win playing ugly but that's alright because we're into the semi-finals. If you invest into the game like that, you should enjoy winning, so don't be sad.'
"Even though I may have been pulling whatever's left of my hair out up there tonight, in the end I was still pretty happy with the character they showed to come back."
And it was some comeback. Stade were 16 points adrift with just over a quarter of the game gone and it looked as if their history of continental heartbreak was about to continue.
But two superb scores in quick succession, the first from Scotland full back Hugo Southwell and the second from blindside flanker Pierre Rabadan, gave Stade a much-needed kick start prior to a hugely improved second-half showing.
Indiscipline may have kept Montpellier in the game in the final 40 minutes but the character shown by the hosts, particularly at a time when domestic inconsistencies are leading the French media to continually and mercilessly criticise the Parisian giants, ensured Cheika left for home a happy man.
"It was a yo-yo game and we made far too many mistakes. But when we went behind 16-0, considering everything that's going on, we could just have fallen away and said 'let's go on holidays'," added Cheika.
"But they hung in there, stayed tough and we scored four tries to one in the end.
"Unfortunately, our discipline let us down so we ended up only being four points in front but I think over the picture of the whole game we probably deserved to win by a bit more.
"We've been working on a big programme of the Club being the main thing. Maybe over the last few years it's been a bit more about this player and that player. We're starting to play a bit more for the Club again, playing for the jersey and toughening up.
"We've been under a lot of pressure. We've got a small squad and we're often measured against Stade's Championship-winning teams. Everyone's been saying we're hopeless. Everyone wants to put the knife in. Sometimes we have been poor but sometimes we've been really good too.
"There's a lot of bad talk going on around the club and lots of bad rumours but one thing that's been good is that we've stayed pretty zen amongst it all. We've been quite solid. Max (chairman Max Guazzini), the finance guy, myself, the management, the players, the staff - everyone knows we've just got to hang in there together.
"We've still got to knock a few things down to rebuild, but we've got a plan and I've seen enough positive signs in the matches that we've had and in what's happening off the field as well to say that we're on the way."