Youngsters Ethan Ampadu, Charly Musonda, Kenedy and Allan Christensen were all handed starts by Conte, while Danny Drinkwater made his debut for the club.
“The performance was very good, especially in the first half when we created chances to score,” Conte told reporters after the win.
“In the second half we suffered a bit – it’s normal when you play against Everton.
“Everton are a good team and have just changed the coach and usually in this type of situation, the players want to try to give more. For this reason, this game was dangerous for us.
“But I am very happy – tonight I saw a lot of positive things – the young players’ performance. Charly Musonda, Kenedy, Ampadu – he is only 17 years old – they all played a very good game.
“It is important to trust in these players and I am happy because I had a good answer, the answer I was waiting for. The other good news was to see Danny Drinkwater.”