The result moved the Ospreys to within four points of Glasgow, who currently occupy the final play-off position.
The triumph over the Dragons extended their extraordinary record against their Welsh rivals, which now stands at 15 games unbeaten.
However, the Wales and British Lions lock was downbeat after securing the hard-fought 20-10 win.
He said: “With an overview of the RaboDirect PRO12, particularly for us this year, we’ve slipped out of top four contention but we’re still pushing and have a chance if some fixtures go our way.
“We played so well at times and got so little back for it. We’re rueing the opportunities we missed as we just squandered them really.
“I said at half-time that territory and possession were massively in our favour but I think we might have just got a little bit excited.
“No disrespect too the Dragons but we were surprised that we squandered our opportunities but we got the win at the end.
“We’re not really content with the win but it’s a win all the same and that’s what we needed with where we’re at.”
And Jones, 28, thinks that Judgement Day II has been a success – despite his team failing to clinch a crucial bonus point in the play-off race.
He said: “The day was really good, the day itself was great. The way we’re feeling is pretty bad but there is probably two sets of fans thinking it was a great game and really good spectacle.
“With the score at 0-0 at half-time it was game on, but as I said we’re disappointed with the opportunities we missed, but overall I think the occasion lived up to what it could have been.
“It’s a good product and it’s nice to be a part of. I said before that it would definitely be a good idea to have two Judgement Days in one season.”
