The striker was often sidelined under Roberto Mancini, but was given a chance to impress by the new manager and repaid him with a sizzling display in a comprehensive 4-0 home victory.
Neville said it was one of the best performances he has seen from Dzeko in a City shirt and he feels that the departure of Mancini and the absence of disruptive influences such as Mario Balotelli will have a positive impact on the dressing room.
"Dzeko's interview at the end was a little bit telling," said Neville on Monday Night Football.
"He was sort of saying he wasn't that happy at the end of last year and the manager didn't give him any confidence. He was one of the ones he was harsh with at times.
"He had a great run of goals from the bench, but Roberto Mancini never really went with him. He looks like a completely different character now. He looks like the player they signed.
"The only thing missing from his performance was a goal. He looks like a team player, he works hard and he'll run the channels and do the ugly bits.
"I thought they looked a happier bunch in that one game. It's early days and they'll face tougher tests in the next few weeks, but that was a pretty positive start for Pellegrini and City."
Pellegrini paired Dzeko with Sergio Aguero - instead of summer signing Alvaro Negredo - for the Newcastle clash and Neville was impressed by both of them.
The Argentinian scored 23 goals in City's title-winning season, but just 12 last term and the Sky Sports expert says there are signs of him returning to his best form again.
He added: "In the first year he was here, his movement was world-class and he was a player you wouldn't want to play against.
"Last season was a dip for him. They'd won the title, he'd scored the winning goal and he was on a high and sometimes you do get a little bit of a dip after that.
"This year he has started off on the right foot and I expect a massive performance from him this year."