Defender Leonardo Bonucci described their performance against the Danish champions as "close to perfection" while goalkeeper Gianliugi Buffon said it showed that few teams could match the Serie A champions on a good day.
"We are Juve and we have to try to win every game we play," Bonucci told reporters.
"We played a very good game, this was a great Juventus. I think we were close to perfection."
Assistant coach Angelo Alessio, who is standing in for the suspended Antonio Conte, added: "Everybody played well and the result is clear: it was a great performance."
Buffon said: "This was a very convincing performance that showed if Juve step on to the field with the right ingredients then few teams in the world can keep up with them."
Juve's relief was certainly understandable given the circumstances.
They had lost a 49-match unbeaten Serie A record against Inter Milan on Saturday and had drawn their last nine European games, including the first three in Group E against Shakhtar Donetsk, Chelsea and away to Nordsjaelland.
Yet, just as talk of a crisis following Saturday's defeat may have been exaggerated, they appeared to be over-reacting to their win against inexperienced opponents who had already conceded seven goals in the group and scored only one.
Juve are still likely to need four points from their last two games, at home to Chelsea on November 20, and away to Ukrainian champions Shakhtar Donetsk, if they are to progress.
When Andrea Pirlo is at his majestic best and Arturo Vidal and Claudio Marchisio are in full flow in midfield, they are certainly a formidable outfit especially with a home crowd behind them.
But they tend to play their best football in fits and starts, struggling to maintain their rhythm for the whole match, and are prone to lapses in concentration.
With a squad which lacks strength in depth, they are also vulnerable to injury and loss of form, with Pirlo especially difficult to replace.
Question marks also hang over the strikeforce.
Alessandro Matri has struggled for form and goals this season, Mirko Vucinic infuriates fans with his individualism and Sebastian Giovinco has shown only exasperating glimpses of the form which earned him the nickname Atomic Ant, although he scored a superb third on Wednesday.
Danish forward Nicklas Bendtner, signed from Arsenal in the close season, has struggled to settle and has barely played.
Juventus attempted to bring Sergio Aguero to the club last year but, with UEFA's financial fair play looming and Serie A in financial difficulties, they have discarded any further attempts at big-name signings.
"I would say that is an almost utopian idea, not just for Juventus but for any of the Italian teams," said sporting director Giuseppe Marotta before Wednesday's game.
"I think it would be very unlikely for a club to invest more than 30 million euros for a player."
