A Paulo Dybala goal in the first half was enough to secure a third straight Group H victory for Juve, who are five points clear of nearest rivals United in the section .
The scoreline did not reflect Juve's dominance at Old Trafford , however, with David de Gea making a wonderful one-handed save to deny Cristiano Ronaldo on his United return.
And while former Juve midfielder Paul Pogba hit the post with a late effort, United could not find a way to break down the Serie A champions , with Mourinho hailing the performances of Giorgio Chiellini and Leonardo Bonucci .
"Juventus are champions for seven years, I think seven years in a row, two Champions League finals in the last four or five years and not happy with what they have, they want more, they want more," Mourinho said at his post-match news conference.
"They had [Gonzalo] Higuain, [Mario] Mandzukic, Dybala, they want more. They want Ronaldo. They had [Andrea] Barzagli, Chiellini, [Daniele] Rugani, they are not happy, they want more, they want Bonucci. And they go for the best players in the world.
"So big, big club with a big past but with also a big desire to have a big future and everything they put there to try to win, I don't say the Champions League, I think to win the treble, that's what they want.
"Because normally they win at home. But the treble until now, unfortunately for these fellows on the other side, is our [Mourinho's former club Inter's] treble, yet I think they are really close to it."
Responding to another question about United's progress, Mourinho added: "To go to the Juventus level? Barcelona level? Real Madrid level? How can you reach that level? Manchester City level? How can you reach this level?
"Yes [with the best players]. It is not also easy. Because many of the players they belong to these top teams, so we work with what we have and we try to improve with what we have. For example, today the way I say amazing Chiellini and amazing Bonucci, I have to say Chris [Smalling] and Victor [Lindelof] had a very positive game.
"It is the first time Victor plays a game of this dimension, Victor had a positive game, Luke Shaw - Champions League at this level of match - so good experience for some of the boys. [Marcus] Rashford, [Anthony] Martial, [Romelu] Lukaku, I think it's the second season he plays in the Champions League too.
"So we work, we work hard, we try to improve our players but quality is quality. And, again, I repeat quality in football is everywhere, when I say quality I don't say just a creative player or just a beautiful player. Chiellini and Bonucci beautiful, absolutely beautiful. But my boys, so happy with what they did."