The striker came off the bench to curl home from almost 30 yards out in the 89th minute, securing a desperate 1-1 draw for his side at Stamford Bridge.
"I think City and Liverpool are a step forward of us, but I think also we are more close than I thought one week ago", said the Italian.
Whilst the headlines will be dominated by Sturridge's simply majestic equaliser and yet another superb performance from Chelsea talisman Hazard, what is worrying for Liverpool fans is that it is ultimately distracting from yet another tepid performance from main man Mohamed Salah. When he came in the dressing room after 20 minutes or so, it was pretty loud.
"He's such a threat still and it's really good".
Chelsea are also still to taste defeat under Sarri, and the former Napoli boss says the Blues can be buoyed by their display.
Eden Hazard can add Chelsea team-mate Jorginho to his ever-growing fan club, with the Italy worldwide considering the Belgian to be "amazing" and the best player he has played with. "He's a great player, a legend of the game".
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Having failed to mount any kind of defence of their title last season with Antoniuo Conte in charge, Chelsea look like a team again under Sarri and Hazard's spellbinding early season form is a sign of the improving mood at the club.
Hazard is the Premier League's top scorer this season with six goals, and the 27-year-old has scored those six goals from just nine shots on target.
But the dead eye for goal the Egyptian showed last season to earn that accolade ahead of the likes of Lionel Messi and Hazard, was missing before he was replaced by Xherdan Shaqiri 25 minutes from time.
After flicking the ball to Mateo Kovacic, the ball was held up by the midfielder as Hazard ran through unchecked to receive it back before striking low past goalkeeper Alisson. But I prefer if we can.
Chelsea sit two points further back after a thrilling encounter, but, like Liverpool, remain unbeaten.
"When you are winning 1-0 at home and concede at the end, you can be sad", Hazard said.