Mark Jones’ side lost at Stadio Monigo and now have little margin for error if they are to challenge for a play-off placing come May.
Centre Keiran Williams scored tries in both halves but Ross Moriarty, who had earlier been sin-binned, was shown a red card in the 64th minute.
The Ospreys number eight was dismissed for a dangerous clearout when the score was 24-12, a costly offence that led to a Jack Walsh try being chalked off.
Benetton, though, were worthy winners after scoring five tries in Treviso through a double from wing Onisi Ratave, Tongan hooker Siua Maile, Argentinian international Ignacio Mendy, and fly-half Jacob Umaga.
Replacement scrum-half Luke Davies scored Ospreys’ third in the 80th minute but they were unable to come up with another for a pair of bonuses.
“It was a very physical game, and we anticipated that before kick-off,” said Jones after the match.
“I thought that we were far too error-ridden in our general play, set-piece and phase attack.
“We gave the ball up too easily, and Benetton brought a lot of physicality around that. I thought we were prepared for it, but they were very strong.
“We weren’t at the level required to maintain possession of the ball, and we spent a lot of time without it in the first half. You could see the fatigue and energy draining from us as a result of that.
“I also saw lots of opportunities that we created, and we should have scored two or three tries. We should be going home with some points – one or two, maybe.”
Ospreys are now six points back on eighth-placed Bulls in the URC table and realistically must win against Connacht in Galway next weekend.
“It goes back to accuracy, and we were not accurate enough,” continued Jones.
“Obviously, spending 30 minutes with 14 players is always going to be tough against a team as good as Benetton.
“The yellow cards were definitely a big factor, particularly when I was just a one or two score game, and then the disallowed try was a big moment.
“I have to credit Benetton, they are a good team. We didn’t play well enough to come to a place like this and get a result.”
[Lead image: Ospreys Rugby]