Roberto Firmino tapped home a second nine minutes into the second-half and Liverpool should have added to their lead as Sadio Mane and Naby Keita were denied by Vorm.
Heaping praise on Chelsea's top scorer this season, Sarri said, "I thought he was one of the best players in Europe, but now I change my mind that he is the best".
There will be some regrets at Stamford Bridge that Salah is now shining at Liverpool, but he could not get into the Chelsea team because Hazard was the main man. Salah surpassed Hazard last season, but the Belgian is preparing quite the response to a man who swept the Premier League awards board.
But Sarri wants his star man to spend more time closer to the opposition goal rather than dropping deep to get attacks started.
Cardiff couldn't have asked for a better start when a well-worked Joe Ralls free-kick was headed across goal by Sean Morrison and bundled in at the back post by Bamba.
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He said: 'I think Hazard can improve more.
'When we have the ball in our half and he touches the ball five times or six times, so his actions it shows he spends a lot of energies, and can have more energy in the last 25 metres.
The Blues now have five points more than they had at this stage last season as they prepare to start their Europa League campaign.
"Hazard can improve more". Cardiff went into the global break with a 3-2 loss to Arsenal, a game that earned the Gunners their second win of the season.
The Blues top the table on goal difference from Liverpool, who also boast a 100 per cent return from five matches. To close that gap in only one season is very hard.
He hit the bottom corner after dancing round two defenders to shoot low in the 37th minute, then latched on to another Olivier Giroud layoff in the 44th.