Goals from Alessandro Matri and Fabio Quagliarella converted a 3-0 first-leg advantage into a 5-0 aggregate victory over Celtic and at the final whistle Juve found themselves in the quarter-finals for the first time since 2003.
Conte praised his heavily-rotated team for producing another accomplished display while stressing the importance of further concerted effort to realising a potential Serie A and European double.
He told juventus.com: "Congratulations to the lads for everything they've done up until this point, but also to the fans for the support they gave us.
"Celtic's supporters were also magnificent and set an example for the way in which they urged their team on right until the end.
"We changed a lot for today (Wednesday) and I'm happy with the performances of those who played. We've qualified for the next round without conceding and both strikers got on the scoresheet.
"We now progress into the quarter-finals and the Champions League is a dream we want to continue to chase.
"We're favourites in our domestic championship, and rightly so, but we've still got plenty of fixtures ahead of us for which I'll need all of my players, now more than ever."
Veteran goalkeeper Gianluigi Buffon echoed his coach's sentiments concerning the formidable strength of team spirit currently driving them forward.
"Our strength is the fact that we are experiencing a tactical awareness we didn't have before," he said.
"That allows us to go anywhere and play our game. You can win or lose, but in the toughest moments, the group has an extra weapon to call on - our playing style.
"We always look to impose our style of play but in previous Champions League campaigns we may have relied too heavily on individuals. But by sticking to a game plan, you actually allow players to shine even more.
"We are in the last eight which is no mean feat when you think that that just 15 months ago we finished seventh in Serie A for the second year in a row."
Defender Leonardo Bonucci is another Juve star allowing himself to dream of reaching this summer's Wembley final.
Juve lost their last final outing to AC Milan at Old Trafford in 2003 and the Rossoneri remain in the competition alongside other giants including Real Madrid, Bayern Munich and Barcelona.
"The dream continues," Bonucci said. "Anything's possible when you get to this stage, you just need a bit of luck to go all the way. There's little difference between the sides, they're all very strong."