Paddy Jackson edged out Dorian Jones on points from the tee, but the game was lost for the Dragons in their inability to breach Ulster's line, despite prolonged periods of pressure at either end of the game.
The result drops Jones' men down to ninth in the GUINNESS PRO12, and while he believes that they are not far from the winning formula, the 46-year-old admits they need to be more clinical.
"The positives are the performance although it was close but no cigar," he told WalesOnline.
"Last season our driving maul was successful in creating tries for us. What it does is allow you to build your game from it, but we didn't convert those drives into tries against Ulster.
"They were pretty good at defending those drives. Having said that, we have to take our chances because we put Ulster under a hell of a lot of pressure but failed to score.
"It's difficult to go into the changing room and criticise the players after the effort that they put in. We've got a few improvements to make but if we keep that attitude each week then we won't be far away.
"It's in our game in Wales to score more tries - the Scarlets are averaging about 25 points a game - but we've not been able to do that yet at the Dragons.
"It's a case of more hard work until we get that right. With Europe starting next week and my old club Sale Sharks coming here in an attractive Anglo-Welsh fixture for our supporters, it's important we continue to learn."
To buy tickets for the GUINNESS PRO12 Grand Final click here. Also follow us on Facebook, join the conversation on Twitter, sign up to our YouTube channel for extensive match highlights and sign up for our newsletter for regular updates on the GUINNESS PRO12.
63x46.png){kind=logo}