Scott McTominay and new signing Kevin de Bruyne struck for the defending champions.
Conte said afterwards: "I asked the boys to make a good impact, to send a signal, first and foremost, to ourselves, that nothing has changed since last year. And nothing must change in terms of focus, dedication to the cause, and the desire to work together in both phases.
"I had good feedback on this; from the start, we made an impact and took the game our way. We did it against a very well-coached team, with ideas and with players who can cause damage, like Berardi and Laurienté, who can create danger on the counterattack, and Pinamonti himself. From this point of view, I'm moderately happy. We know we have work to do, and we're doing it. We must continue on this path, not forgetting all the positive things that last year led us to achieve something extraordinary and unexpected."
On De Bruyne's debut, Conte continued: "Kevin was the only player who made the starting lineup today compared to last year. I've said several times that when you try to complete the squad for the new season, and we had to do that and are doing that, it's inevitable that when players arrive from other teams with different ambitions, it takes time to settle in and adapt.
"And let's not forget that we have a Scudetto on our shirt, and that's tough: it's one thing to play in other situations, it's another thing to play at Napoli and feel the pressure, like the one we've been under since the start of the season. I think Kevin is doing well, adapting to what's asked of him. We're trying to bring out his strengths, I try to bring out the positive qualities of all the players, trying like a tailor to find the right formula.
"We've been working on it for two weeks, and something has shown in this regard. We need to keep working and never lose the unity that is the true strength that last year made us achieve something unexpected and extraordinary."
Conte also handed a debut to Antonio Vergara and added: "Antonio Vergara is a young player from Napoli's youth system; last year he had an excellent season with Reggiana. He's a player who will be part of the squad, especially since he won't affect the squad numbers, being a youth player. So, he's welcome. I don't care if someone is young or not."