Hazard outran the City defence in an outstanding performance at the Etihad Stadium and Mourinho was quick to lavish praise on the Belgium midfielder.
The 23-year-old winger, who has scored 11 goals for the Blues so far this season, told the BBC's Football Focus programme: "I'm very happy because it's very pleasing when a coach gives praise but I'm still aware of what I need to do to make the next step up.
"It's a nice compliment but I'm not going to rest on my laurels
I know I have to keep working hard every day.
"It was a great atmosphere in the dressing room (after the match) but we weren't getting carried away because we know that there are plenty of big games ahead.
"We beat possibly the best team in the league, but we know that if we then go on to lose against Newcastle then it's no use whatsoever.
"It's up to us to pick up the maximum points from the games that are coming up."
Hazard, who made the switch to Stamford Bridge from Lille in the summer of 2012, was humbled by talk that he could be the best young player in the world, but predictably looked to Cristiano Ronaldo and Lionel Messi as the benchmark.
There's lots of tough young players out there," he said
"Yes, I think I'm up there with the best but I hope people will eventually take away the word 'young' because that would mean I've moved up another level.
"I think to get to their (Ronaldo and Messi) level I have to work extremely hard
Those players are on another planet because they score two or three goals every game.
"I hope to be like them one day and it's up to me to find ways to score, just like they do, every game."
Hazard is enjoying working under Mourinho and hopes to keep up the hard work at Stamford Bridge to reach the standards Ronaldo and Messi have achieved.
He said: "He's made me focus on my work ethic even more
He aspires for one thing - that I become like them one day.
"It's time for me to work hard together with the coach and the club to achieve that objective.
"Results have been going well so he is happy and perhaps a little more relaxed
I think as long as we're all working hard, he's happy
And the most important thing is to make him feel happy."
Source : PA
Source: PA