And while it is the Parisians who march on to the final four for the second season running, Mieres and co have more than proved their worth as they now turn their attentions to securing a Heineken Cup spot for next term.
"We now realise that we can beat anyone," said Mieres, who kicked 12 points in a 22-17 defeat and has been central to Exeter's rise to fifth place in the Aviva Premiership standings.
"It was a really good all-round performance. We kept the ball well because we knew we couldn't give Stade possession as they are so dangerous.
"We hung on to the ball for several phases and we built our game well and gained a lot of metres from that, but we didn't score as many times as we should have.
"A lot of credit must go to them because they played some really good rugby as well but rugby can sometimes be unfair and I think we deserved to win.
"Stade don't often lose at this stadium, though, and this gives us a lot of confidence."
Despite this being just their second attempt at European competition following their promotion to the top flight of English rugby last season, Exeter saw off French heavyweights and former Heineken Cup finalists Perpignan in the pool stages.
Rob Baxter's men also beat the vastly more experienced Newport Gwent Dragons both home and away before falling just short of the most memorable victory in their history against a Stade side packed with star names.
And rather than feel sorry for themselves after failing to turn their first-half dominance into a more substantial lead in the French capital, the Chiefs will now aim to complete a top six finish back home to ensure they join Europe's elite next time out.
"We've now got three really tough games in the Premiership with Worcester, Northampton and Saracens but this bodes well for those matches and we know we can push on," added Mieres.
"If we get out there in the right frame of mind, look to play and look for the right result, we can achieve a lot of good things in these final three games.
"It's just our second season in Europe and the Premiership and we've realised that we're not a second division team. We're a top-level Premiership team and we can play anybody.
"We have a good game plan with good players who can execute on the pitch and we've been showing that all season. We've beaten Leicester twice and we've been playing some really good rugby. We showed that again against Stade."