After two years of finishing fifth in the competition, the Welsh region are desperate to return to PRO12 play-off rugby.
And after a thumping opening-weekend win over Benetton Treviso they made it two from two on Friday night, edging past Newport Gwent Dragons at Rodney Parade.
However, Gibbes insists a productive start to the campaign is no more than that, as Ospreys turn their attentions to Edinburgh's visit next weekend.
"We aren't getting ahead of ourselves," he said. "We've got a young side and we can't take anything for granted. We've got to go into every game with a mindset that we're punching above our weight every week.
"What is important is that we've still got plenty to work on so we are definitely not getting too far ahead of ourselves.
"Result-wise, we got that, but we made it hard work at times and there's a lot to work out before we have Edinburgh coming at us a week Sunday. We need to get ready for that, one game at a time."
Ospreys prevented their hosts from crossing the line on Friday night, while Rhys Webb and Eli Walker each dotted down in Newport.
And it was their resilience towards the end that left Gibbes with the impression that this young squad can go far.
He added: "For them to show that grit, and to dig in particularly in that fierce last ten minutes, we're proud of that.
"I think these games come down to one or two opportunities, they don't come very often and you've got to take those.
"There were some good performances across the park but overall as a team, while we are happy to come here and get the win, there's lots to work on."
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