The 5-1 win set up a fourth round clash at home to Everton, but, despite facing Premier League opposition, Chelsea could field a similarly youthful squad.
Conte said: "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?"
Michy Batshuayi scored a hat-trick, while Kenedy and the impressive Charly Musonda were also on target for Chelsea
Tendayi Darikwa scored a late consolation for Championship Forest.
Eden Hazard delighted on his first start of the season after his broken ankle, while Conte assessed the Chelsea youth.
Chelsea academy graduates Musonda, Andreas Christensen, Jake Clarke-Salter and Dujon Sterling featured, while Ethan Ampadu became the first Chelsea player born this millennium, a week after his 17th birthday.
Conte added: "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."
Conte praised Musonda, whose pace frightened Forest, but says the slight Belgian has work to do to be ready for the rigours of the Premier League.
The Italian said: "I think Charly played very well
He's trying to work a lot to improve his physical impact.
"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."
Kenedy's Blues career looked like it could be coming to an end when he was sent home from the pre-season tour to Asia following some ill-advised social media posts on China
He apologised and has been reintegrated into the squad.
The Brazilian scored Chelsea's first and his first goal since March 2016 when he ghosted behind the Forest defence to meet Antonio Rudiger's cross with a side-footed shot that beat goalkeeper Stephen Henderson.
Conte was asked about the pre-season controversy, but side-stepped questions on it, preferring to focus on Kenedy's performance.
"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."
Chelsea's next midweek match is next Wednesday's Champions League tie at Atletico Madrid.
David Luiz is serving a three-match domestic ban but is poised to be included despite sustaining a fractured wrist in last Sunday's goalless draw with Arsenal when he clattered into the advertising hoardings at the end of the first half.
"He must be okay," Conte said.
"David is an important player for us
For sure he will be ready for the game against Atletico Madrid."
Forest boss Mark Warburton was frustrated with his side's defending.
"You can't give away soft goals
It's as simple as that," Warburton said.
"We took liberties on the edge of our own box
And against that level of play you will be punished.
"You can't concede soft goals
Unfortunately tonight against really good players we were too soft at times."
Source : PA