But things fell apart somewhat after the break as the Bath scrum gained the upperhand, with three more Tom Heathcote penalties and a late converted try from Mat Gilbert seeing Bath home.
"If our scrum and lineout had been a bit better, I'm pretty confident we would have won," said Jones, whose side have won all four competitive home games so far this season - as well as a pre-season friendly with Bath - but are yet to succeed on the road.
"It all came down to a creaking first phase, that's plain for all to see. There were a lot of very disappointed players in our changing room because Bath just had too much power in the front five, and that's the game of rugby.
"We had people putting their heart and soul into it. It's just disheartening that so many of Bath's points came from our inability to relieve pressure. That meant we were playing catch up without a platform to launch from.
"I thought Paul James came on and changed the game for Bath. We just failed to get our first phase going. We're not going to move forward until we can firm up our first phase."
There were plenty of positives for Jones to take back across the Severn Bridge, though, with his side still capable of causing an upset until Gilbert crossed with just 10 minutes left to play.
Jones spoke repeatedly in pre-season about the need to harbour a winning attitude at the region and the way in which his side reacted to Saturday's defeat showed they are moving forward in that respect.
"I was pleased with many aspects. We came down and competed well," added Jones.
"There were lots of strong performances: Toby (Faletau) was excellent and Richie (Rees) and Jason (Tovey) really caused problems for the opposition.
"Defeat is always hard to take and the boys are disappointed - that's nice to see. We're not going away and accepting defeat now, we're starting to learn. We're moving in the right direction."