Trailing by ten points after a disjointed first 40 minutes, Ospreys appeared to have manoeuvred themselves into a winning position in Palma on Thursday evening.
Justin Tipuric's try just 34 seconds after the restart got the ball rolling before Ashley Beck and Alun Wyn Jones both crossed to put the visitors 27-16 up with 13 minutes to play.
But Zebre came again, Brendon Leonard crashing over before replacement Guglielmo Palazzani confirmed the 30-27 victory in the 82nd minute.
Before the game, the Welsh side knew maximum points would bring them level with fourth-placed Ulster but they would only end up leaving Italy with a single losing-bonus point.
It means Ulster need just one point from their remaining two games with Gibbes admitting his side had let their opportunity slip through their fingers.
"Obviously it's a painful defeat and we need to learn the lessons from it. It's not over yet. Yes we are realistic, but as long as there is a chance, we'll keep going," he said.
"If next weekend we have a sniff then we'll go for it, but we are honest with ourselves and accept that it's an outside chance now.
"You have to give credit to Zebre. We spoke before the game about how they are a vastly improved team and how dangerous they are, and they kept going right to the very end.
"But, I think it's fair to say that we made it easier for them at times than it should be.
"This is a young group, a very exciting group of players, but if they are going to develop into what we think they can, then they need to learn to be more clinical and to handle pressure situations better."
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