The Ospreys captain, Duncan Jones, said his side were disappointed but still determined to make it out of Pool Three after Stade Français punished their mistakes for a comfortable win.
The Ospreys were in contention at 9-7 down at half-time, but second-half tries by the centre Mirco Bergamasco and prop Rodrigo Roncero ended the Welsh region's hopes of a rare win in France.
"It's a disappointed changing- room," said Jones. "We stepped up to the mark, but we were made to pay for one or two crucial mistakes. But it's all still to play for in this competition for us - this defeat has only made us more determined to get out of this group. We have plenty to work on."
Stade were defending an enviable home record, having lost just once here in 25 Heineken Cup games. Their only blemish came when Munster left Paris with a 16-14 win in the 2002 quarter-final, and they duly opened the scoring when the fly-half David Skrela landed a difficult penalty from 40 yards out on the touchline on 12 minutes.
But the Ospreys took the lead less than five minutes later, when their former All Blacks scrum-half Justin Marshall dummied right from the scrum, leaving the No 8 Ryan Jones to exploit a hole. The fly-half Gavin Henson then worked a scissors with Sonny Parker and the big centre handed off would-be tacklers to touch down out wide.
Henson slotted the conversion, but only last-ditch defence kept the hosts at bay, and the pressure eventually told when Steve Tandy pulled a maul down and Skrela kicked the resulting penalty. A professional foul by the former All Black flanker Filo Tiatia then earned him a yellow card, and Skrela landed his third penalty before half-time.
The second half saw Henson miss two more penalty attempts, and he eventually made way for James Hook at fly-half. Ryan Jones found himself offside at a ruck to allow the home side's replacement fly-half, Lionel Beauxis, to put his side 12-7 up.
The sucker punch landed seconds later, when a flowing move cut the Ospreys defence to pieces and ended with Beauxis giving a scoring pass to Berga-masco, the Italy centre, who dived under the posts. Beauxis' conversion put Stade in the clear at 19-7 before the try by Roncero, a front-row replacement, killed off the visitors.
The Ospreys full-back Lee Byrne's late try was no more than a consolation, and the Italy No 8 Sergio Parisse added insult in injury time with a drop goal.
Stade Français: J Martin Hernandez; J Saubade, G Messina (I Corleto, 68), Mirco Bergamasco, C Dominici; D Skrela (L Beauxis, 40), A Albouy (J Fillol, 18); S Marconnet (R Roncero, 56), D Szarzewski (M Blin, 68), P de Villiers, D Auradou (capt; M James, 56), B du Plooy (R Samo, 78), Mauro Bergamasco, S Parisse, R Martin.
Ospreys: L Byrne; N Walker, S Parker, A Bishop, R Mustoe; G Henson (J Hook, 57), J Marshall (J Spice, 74); D Jones (capt; P James, 60), H Bennett (B Williams, 65), A Jones (D Jones, 72), B Cockbain (A Wyn Jones, 40), I Evans, S Tandy, R Jones (Tiatia, 78), F Tiatia (J Thomas, 40).
Referee: A Rolland (Ireland).Reuse content