An impressive kicking display from Jason Tovey on his return from a year with Cardiff Blues saw the Dragons home after Roger Wilson had scored the only try for the Belfast-based side but it was the manner in which the hosts applied pressure at every single opportunity that most pleased their new boss.
"When I strolled in here in June the emphasis was on defence and breakdown, defence and breakdown. We pushed Ulster back, they couldn't get into the position they wanted to and, as always happens in rugby, you get your chances and that was enough," said Jones.
"There's 100-odd rucks in a game of rugby and only 15 or so lineouts so it's important that you coach everybody how to win rucks. There's been a big appetite for that here.
"Ulster failed to deal with our defence. I enjoyed watching Ulster last year: they were a great team and a great attacking side and it was exciting to see them play. That Ulster side was full of confidence and they're three years down the track on their project and we're just starting ours.
"When it was on to go they started kicking, kicking, kicking. You looked at them and thought, 'this is not the Ulster I'm used to'. We pushed them into plan B and it stifled them."
Next up for the Dragons is a trip to Murrayfield to face Edinburgh this Friday, with Jones believing that their Round 1 victory over one of the tournament's big hitters will give his side a real boost.
The former Ospreys coach has talked about his determination to increase the sense of positivity around Rodney Parade and he has told his players they should be hugely encouraged by what they produced in their first competitive fixture.
"We need confidence and belief and this was a tap on the back. I'm sure we can finish higher than 11th this year," added Jones.
"It's not for me to give them that belief, it's for them to grow and really believe it. When a player turns up to a game expecting to win, then you know you're on to something. We're not quite there yet, we've got a lot of work to do, but my job is to bring the best out of these boys and if I can get them playing to their utmost, I'll have done my job.
"This group is growing - these boys were on their backsides last season. There's a lot better to come from us, but we'll play a lot worse teams than Ulster, I can tell you.
"If we'd have lost that game, the performance still would have been a massive positive. If Ulster had won 15-8, we'd have tapped ourselves on the back and thought, 'that's good progress from us."
Wales No8 Toby Faletau could travel to Scotland for his first Dragons involvement since impressing for the British & Irish Lions Down Under, although Jones insists his star player isn't guaranteed a starting spot if he does make the trip north.
"He will be in consideration for selection. I haven't seen enough of him in training yet to know how good he is!" quipped Jones.
"You need to work with players to see what they've got. I've seen him play with the Lions and he looks a decent player, but the other players here are doing well.
"I'm sure Toby will have some involvement, if not this week, then certainly against the Scarlets."