Hazard is Chelsea's top scorer this season with 10 goals and has often swung matches in the Blues' favour with his attacking guile.
But it is his new-found work ethic which has pleased Mourinho most.
"At the age of 23 to be where he is, we can only expect better," Mourinho said.
"(But) let him go. Let the top, top ones at 27, 28, 29 years be where they deserve to be because they have careers of many years at the top.
"And let Eden follow his way, the way he is doing."
Hazard, who Mourinho insisted is not for sale despite rumoured interest from Paris St Germain, has relished the responsibility of taking the initiative for Chelsea this term.
Mourinho knows he cannot always look to Hazard for a spark, but he is happy with the former Lille forward's progress.
"I cannot expect him to be the match-winner in every game; I cannot put this kind of pressure (on him)," Mourinho said.
"(But) we are very happy with him. He has improved a lot in every aspect.
"He was known as one of the worst trainers. He was training to have some fun. Always having a joke. Not top concentration.
"He has become - I don't say one of the best - but a good professional in training.
"He works very hard for the team. He's trying now all the time to be an influence in our game. He's getting this responsibility."
New experiences await for Hazard in 2014 - the knockout stages of the Champions League and a World Cup.
Chelsea are also in contention for the Premier League for the first time since Hazard joined and could go top with a win at Hull on Saturday.
"It's important we are close to the title," Mourinho said.
"It brings a different pressure. The players improve with the pressure."
Mourinho denied he had compromised Hazard's attacking flair by demanding more of him defensively.
"It's never a problem for a person to be more complete than they were before," said Mourinho, who disciplined Hazard for missing a training session earlier this season by leaving him out of the match with Schalke.
The Portuguese believes for Hazard it was a change of mindset that was required for the improved work ethic.
Mourinho tinkered with Hazard's approach through "conversations, feedback, demanding more" and by "showing him the way I think is the right way and even if it isn't the right way, it's the way he has to follow".
Hazard has fine examples to follow at Chelsea in the likes of Frank Lampard, John Terry and Ashley Cole.
All three are out of contract at the end of the season, but no one is in any rush to agree a new deal.
Mourinho said: "They are calm. We are calm. We know that they want to do well this season and we know that they want to stay in the club.
"They know the respect we have for them. They know the contribution they are giving this season, which is different to last season where there were many doubts around Lampard, because he was not playing, and John, because he was not playing.
"This situation is not around so everything is calm. No problems."
Lampard is currently out with a calf problem.
Mourinho added: "It's getting better. I think by the end of the month he's ready."
Source : PA