Chelsea thumped promoted Cardiff 4-1 for their fifth win of the season, keeping their 100 percent record and Sarri became only the fourth Premier League coach - after Carlo Ancelotti, Craig Shakespeare and Pep Guardiola - to win their first five games.
But Sarri is looking for better things from his squad. "At the moment for me Liverpool and Manchester City are better than us," Sarri said. "I cannot change my mind after one match."
Chelsea are ahead of Liverpool on a goal difference of one, and two points in front of champions Manchester City.
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"My target is to be the best team in England but not in one month," said the Italian, who took over from compatriot Antonio Conte in the close season.
"We can improve...We are not so solid as I want in the defensive phase," Sarri said, citing Cardiff's early goal from an unmarked Sol Bamba.
Sarri said that when he arrived at Chelsea he thought Hazard was one of the best players in Europe. Now he thought the Belgian might even be the best. "But Hazard can improve more."
He felt Hazard spent too much energy in the opponents' half, collecting the ball when he could be working further upfield and scoring more goals.
Hazard's first two goals came from layoffs by Olivier Giroud.
He hit the bottom corner after dancing round two defenders to shoot low in the 37th minute, then scored after the Frenchman held up the ball at full stretch in the 44th.
"It's a pleasure to play at the moment," Hazard told the BBC. "We have a lot of freedom on the pitch, and at the moment when we try and do something it's coming off.
"I'm always happy when I'm playing football I just want to do my best for this club who have done a lot for me. I'm always trying to do more - create more chances, score more goals, and today a hat-trick so I will try to do this more."
Hazard put away a cool penalty in the 81st minute after Bamba brought down Willian in the area. Substitute Willian rounded off a satisfying afternoon for the London side with a fine strike from outside the area.
(Reporting by Clare Lovell, editing by Pritha Sarkar)
