The Liberty Stadium side were playing catch-up after tries from Darren Cave and Franco van der Merwe gave the hosts an 18-3 half-time lead.
Ospreys rallied to score 13 points after the break but they could not get close at a rain-soacked Ravenhill.
And Gibbes has told his side they will need to get off to fast start if they are to challenge Leinster at the RDS on Saturday.
He said: “It was a great effort in the second half, yes, and we showed great spirit, but ultimately we’ve only really got ourselves to blame about losing this game.
“In the first half we didn’t put it in the areas where we wanted to and that meant we found ourselves under pressure. They took the opportunities that we gave them. Then, we were well in it for 35 minutes of the second half but just didn’t have enough about us to see the job through in the end.
“We’ve got to keep focusing on getting the performance right, and we’ve got to understand that if you don’t take your opportunities then you’ll lose games.
“Leinster away next week will be another difficult match, we know that, but we’ll work hard in training again this week and look to improve on tonight. It’s another game, another chance for us to show that we are learning, that we are improving.”
The Swansea side remain top of the Guinness PRO12 despite seeing their perfect record slip in Northern Ireland.
But Gibbes wants to build on their second-half performance in a bid to topple Leinster.
He said: “We scored a good try that gave us some momentum, we played in the right areas and we put ourselves in a great position to go on and win it with a quarter of the game left. I think we probably did do enough to win the game but ultimately, we gave them too big a head start in the first half and just couldn’t keep going in those last five minutes.
“That’s a mark of the standards expected of the Ospreys that coming here tonight and being 15 points behind at half-time, we are bitterly disappointed about not closing the game out at the death and leaving with nothing.”
