The England opener top-scored in the game with 47 off 37 balls on a difficult pitch at the Utilita Bowl in Southampton on Wednesday (Thursday AEST).
"That was a good toss to win for us, chasing a target. Really pleased with the outcome there," Salt told Sky Sports.
"Some real good catching. We put the balls in the right areas. Did we do it for long enough? That's one for the coaches.
"I've only played one game, but I'm enjoying the group of lads we've got."
Needing nine off the last five to surpass the host's 7-135, Asa Tribe hit the first delivery from renowned finisher Chris Jordan to the midwicket boundary and then took a single off the next.
Salt, far from his fluent best, then cleared the leg-side fence to complete a six-wicket win.
England bowlers Jofra Archer (0-22) and Adil Rashid (0-18) went for just 40 off their combined 40 balls. Australian allrounder Nikhil Chaudhary picked up 2-19 off 15, but Brave's total proved insufficient.
That was in no small part due to Marco Jansen, who claimed 2-17 off 20, with Aussie offspinner Matt Short taking a miserly 1-5 off 10. Only David Miller (44) and Thomas Rew (41) made any impact, with Chaudhary chipping in with three fours in a 12-ball 19.
Short earlier hit 20 off 15 balls, including four boundaries, before England batter Joe Root's debut for Welsh Fire ended when he was run out for 15.
"Really pleased. Proper captain's knock by Phil Salt," Fire quick Chris Woakes told the BBC.
"We did well, I thought. It's hard to keep someone like David Miller quiet.
"It wasn't a great pitch ... to get over the line in the first game is really nice."
With AAP.
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