Tommy Seymour's late try handed Gregor Townsend's side the points, after a Dan Biggar drop-goal had put Ospreys in pole position.
Ospreys' run-in consists of clashes with Leinster, Newport Gwent Dragons, Zebre and Connacht and, though they must hope Glasgow slip up along the way, Gibbes is keeping the faith.
"There's 20 points to play for and anything can happen," he said. "We've got to dust ourselves down and use the next two weeks to look at the areas where we can change things, where we can improve.
"Yes, the defeat means our destiny has been taken out of our hands but we will go all the way, don't doubt that.
"Can we do it? We know it's going to be tough and accept that people will be writing us off, so all we can do is go out there over the next four weeks and really give it our best shot.
"There's a proud history in this competition and we have to do the jersey justice in these last four games. If we can do that, anything can happen."
And despite defeat on Friday night, Gibbes took plenty of positives from the young Ospreys' display in Glasgow.
"There we so much about the performance to be pleased with," he added.
"We were disciplined, there was real desire and commitment, and we restricted them very well. In the end though, naivety and inexperience cost us at crucial moments.
"We've put heart and soul into that for 80 minutes to come up just short at the end and it's hard on the group.
"We've left a lot of injured players at home and brought a young squad up here, and pushed a good team all the way.
"Ultimately we didn't have enough about us to close it out and that is disappointing, regardless of anything."
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