Italy took the lead through Emanuele Giaccherini in the 32nd minute and held firm until injury time, when Graziano Pelle smashed the ball home following a counter-attack to make victory certain.
There have been doubts as to the quality of the current Italy squad going into the tournament but Conte felt the win over Belgium — currently the top-placed European side in the FIFA World Ranking — showed the Azzurri have the potential to succeed this summer.
“It was a good game, played in the right way and prepared well,” he told Rai Sport in quotes reported by Football Italia. “The lads knew how to suffer under pressure.
“We played against a very strong side who are among the favourites to win the tournament. When there is this kind of unity, we can do great things.
“We haven’t achieved anything yet, but we hope to reach the point these lads deserve. I care that we are a team, nothing else. I have 23 talented lads who are happy with each other.”
He added: “You have to do the extraordinary and not the ordinary if you want to achieve your dreams.”
Giaccherini said Italy’s Group E tie was tougher than it might have looked when he was asked if Belgium had played like a team worthy of being billed as one of the top teams in the world and one of the favourites to win Euro 2016.
“Maybe you didn’t see it but we certainly felt it,” he said of Belgium’s quality. “They’ve got terrific players in one on one situations who can hurt you at any stage of the game.
“So we had to do even more than we normally do. And when we had the ball we had to try to hurt them. That’s what the coach asked us to do.”
Giaccherini’s goal came following a superb throughball from Giorgio Chiellini, and the Juventus defender told Sky Sport Italia: “I always did try that kind of pass and doing it regularly leads to improvement, as I’ve done it quite a few times at Juventus and now for Italy.
“Fortunately, Giaccherini had that fantastic first touch for a great goal.”