And Jones, who left London Welsh in the summer after guiding the Exiles to a year in the Aviva Premiership, wants to see improvement from the off, even though the Dragons face last season's beaten finalists first up.
"It's going to take time to grow but what we are looking for from Friday night is an enthusiastic performance from players who I'd like to think will play with a lot of passion coupled up with some accuracy," said Jones.
"We're looking forward to a big home crowd against what I'd say is the best team in the PRO12. We need all the support we can get to create enthusiasm and belief in the squad.
"Only three-and-a-half months ago the Dragons finished nearly bottom of the league so we're not stupid, we know we're not going to turn things around immediately.
"We've played one friendly (an impressive 22-20 win over Bath), which is not ideal, and we are expecting a few more questions than answers after the Ulster game, which is quite common for coaches. What's important is that, no matter how the result goes, we analyse ourselves and keep improving."
The Dragons have finished as the fourth Welsh region in the PRO12 for the past three seasons since ending up above the Scarlets in the 2009/10 campaign but Jones is keen to instill a greater self-belief in his new side this term.
Self confidence could be the key to improvement so former Ospreys coach Jones is determined to banish any negative thoughts ahead of what he knows will be a tough opening fixture and a challenging campaign over all.
"You'd be surprised that people are still talking negatively on the back of last year so I'm trying to stop that," added Jones.
"Players are subconsciously using negative language. They don't realise it but it stands out to me. It's no secret that Gwent rugby has had difficulty with being positive, but we're here to change that.
"I'm used to working with winners and champions and I'm going to turn these guys into winners and champions as well. That's why a good performance is important against Ulster: we need to start being confident and believing in ourselves."