Sean Holley rued the Ospreys' missed opportunities as their qualification hopes are in the balance following defeat to Perpignan in Pool Three.
Shane Williams 58th minute strike launched a brave fight back to keep the Welsh region in the hunt despite the loss in the south of France.
Fellow wing Jonny Vaughton added a second try eight minutes later which leaves them needing to beat Leicester Tigers at the Liberty Stadium next weekend.
The visitors trailed by 17 points following Henry Tuilagi's try in the 51st minute before the Ospreys recovered in style to gain a losing bonus-point.
Ospreys coach Holley said: "There is disappointment in the dressing room. We had a huge chance to win this game. We came out with a positive attitude and we looked dangerous in the first half but we weren't clinical enough.
"We lacked accuracy with the last pass but we know what we need to achieve next week."
