Hazard hit twice in seven minutes just before the break to cancel the initial Sun Bamba clash for the hosts at Stamford Bridge before completing his hat-trick from the penalty spot to take his season tally to five goals in just three openings
But Sarri wants his star man to spend more time near the target of the opposition instead of falling deep to begin the attacks.
"The danger can improve more, I think that it can spend less energy than now at 50 or 60 meters from the objective of the opposition," added the former head of Napoli.
"I told him … you can score 40 goals for me but you have to spend less energy, you have to play in the last 25 meters."
And Hazard praised freedom. Sarri's organization has offered to move forward and try to improve his best record of 19 goals in a season in English football.
"(He) just wants us to play and look for space between the lines so Jorginho, Mateo Kovacic and Cesc Fábregas can find us," said Hazard.
"We have a lot of freedom on the pitch, and the moment we try to do something, it's coming out."
Chelsea rejected the interest of European champion Real Madrid for Hazard after the player declared his interest in moving forward after the World Cup.
And that resilience could still generate an unlikely title challenge after finishing 30 points behind Manchester City last season.
The sumptuous blow of Willian for the fourth place of the Chelsea surpassed to the Blues in front of the Liverpool in the part superior of the table by difference of goals with City to only two points more behind back.
But Sarri insists that the champions of last season and the finalists of the Champions League remain the benchmark for his team.
"My goal is to be the best team in England, but not in a month, maybe a season, maybe a little longer, but our goal is this one.
"At this moment, for me, in my opinion, Liverpool and Manchester City are better than us."
The feeling of being overcome is what Cardiff can get used to, as he did not manage to significantly strengthen himself during the summer in his return to the top flight.
Neil Warnock's men have collected just two points in 0-0 draws with a man advantage against Newcastle and Huddersfield from their first five games.
"We have to learn fast because these superior teams punish you," Warnock said.
Cardiff could not have asked for a better start when a well-worked Joe Ralls foul shot was directed through the goal by Sean Morrison and tied by Bamba.
However, they had no response to Hazard's trick when he put a ball in the path of Olivier Giroud and then shot the return pass of the Frenchman to the far corner.
Hazard had the help of a detour to put Chelsea ahead from close range and gave the home team room to breathe from the place after Willian was knocked down by Bamba.
Moments later Willian capped the defeat with his own moment of magic with a wonderful 20-yard effort that doubled in the top corner.