The three-time competition winners will now travel to Paris on the weekend of April 3/4/5/6 for a last-eight tie that would appear just as tasty if you were told it was in the knockout stages of the Heineken Cup rather than the Amlin.
"We are now going to play against Stade Francais away, and the juices will really flow for something like that," O'Shea told Sky Sports.
"I think it has made a big difference to the Amlin tournament with (three) Heineken teams coming into it. Stade Francais versus Quins is a pretty good game!
"We're delighted to be in it. Come April you want to be playing in the Amlin, you want to be one of those 16 teams in Europe still. It meant a lot to us three seasons ago and it would mean a lot to us again, but Stade away is a massive ask."
Quins finished runners up to last season's beaten Heineken Cup finalists Clermont Auvergne in Pool 4 having been in with a shout of winning the group the week before last.
Victory over Clermont by more than seven points would have seen them head to Wales knowing another victory would have sealed top spot, but Clermont over-turned a 10-point half-time deficit to reiterate their credentials as potential continental kings.
Just to be in the mix for the last eight in either competition required a huge effort from Quins, though, given that they lost their first two games in the tournament, at home to the Scarlets and away in Clermont. Back-to-back victories over Racing Metro gave them hope of a remarkable recovery, before Clermont spoilt the miracle moment at The Twickenham Stoop.
"I said to the guys that, mentally, to come back from the disappointment of last weekend when we had the opportunity to beat Clermont Auvergne, I don't think you should underestimate how much it took for the group to come down here and finish off," added O'Shea.
"You're always learning in the Heineken Cup, aren't you? We started this tournament incredibly poorly losing at home to the Scarlets. We've won at Scarlets, we've got a try-scoring bonus point in winning away at Racing and a losing bonus point at Clermont.
"I think there were loads of pools of death in the Heineken Cup this season. We've won two away games, and I am delighted that we are through. To finish as one of the best runners-up in such a tough pool is a real credit to the guys."