A soft start with Huddersfield, Arsenal, Newcastle, Bournemouth, Cardiff and West Ham in his first six Premier League games have helped Sarri settle in.
However, Hazard insisted he is more concerned with trying to win silverware, than achieve any specific goal tally.
While Trent Alexander-Arnold has returned to training, Klopp refused to comment on whether fellow defender Virgil van Dijk will be available after the Dutchman suffered a rib injury in last week's 3-0 win over Southampton.
Naby Keita put in a better performance at Anfield but I still think he'll drop out with Jordan Henderson and Georginio Wijnaldum recalled to the starting eleven alongside James Milner. If we have one 100 per cent challenge, or four or five, then Eden Hazard can't do what he did.
Sarri has consistently played down his team's chances of lifting the Premier League trophy this season, but he is far more confident that Jurgen Klopp's men possess the requisite quality.
"It will be intense", said Klopp.
"Me and Alisson work together on a good basis, our relationship has been good ever since we came together and then we've got a few younger boys who are pushing us forward as well".
The game is a big test for the Reds who are looking to maintain their flawless start to their Premier League season. He is happy with getting two assists and the team winning. The sale of Andy Cole to United was a major factor in their downturn and they only won two of their last nine league games, finishing in sixth place. With all the things Chelsea did, in the end they needed a free-kick - maybe offside, maybe not, it's not important - and the world-class situation of Hazard to win the game.
Liverpool'take on champions Manchester City next weekend (Dave Howarth/PA).
The pair shook hands but cameras showed Klopp frustratingly gesturing at areas of the pitch towards a sheepish Shaqiri, who was one of Liverpool's better performers on the night.