The 'Blues' ran out 5-1 winners thanks to goals from Michy Batshuayi (3), Kenedy and Charly Musonda before Tendayi Darikwa bagged a late consolation for the Championship side.
Conte fielded a much-changed side, giving valuable game time to the returning Eden Hazard, as well as "academy graduates" Musonda, Andreas Christensen, Jake Clarke-Salter and Dujon Sterling.
17-year-old Ethan Ampadu became the first Chelsea player born this millennium when he came on for Cesc Fabregas after 55 minutes.
Speaking after the game, Conte said that the scoreline represented a job well done and seemed to suggest that he would continue to use young players in the competition, saying: "We are a great club, for this reason, every competition is important to us. If we answer like this tonight, why not continue to give the opportunity to these players?
"I have had the possibility to give a chance for the young players from our academy. I think this is very positive. For sure a good night for us.
"I hope this type of game, this good performance improves their confidence and it's important now to continue in this way.
"When I have this type of answer, I'm very happy. I understand every single player is ready to play."
The Italian singled out Belgian winger Musonda for praise, with his pace proving a thorn in Forest's side all night.
"I think Charly played very well. He's trying to work a lot to improve his physical impact," Conte explained.
"He's a talented player and he has to continue in this way. When there is the opportunity, the chance, to help us, he must do this."
Brazilian defender Kenedy was also praised for his performance, just months after many thought his Chelsea career was over after he was sent home from the club's pre-season tour of Asia after accusations of racism.
"Kenedy played very well," Conte said.
"He's working very well, he's working a lot. When there will be the opportunity, a new chance, he must exploit it."