"We need to move the ball quicker I think", said Sarri, who took over as manager in the off-season after Antonio Conte's departure.
The Blues threw everything forward in pursuit of a winning goal, but Wets Ham hung to claim a vital point.
'We have to work and then, maybe, in one year we will be at the same level as Liverpool'.
Chelsea failed to maintain their 100 percent record after West Ham chiselled out a goalless draw at the London Stadium on Sunday.
'It will be a really hard match, ' said Sarri.
Felipe Anderson was quick to seize on a loose ball and played in Antonio, who blasted over with his left foot. We are improving in the defensive phase.
Sarri is not convinced Chelsea's Europa League trip to PAOK had anything to do with Sunday's sluggish performance, though he does not see why the Premier League can not do them a favour with match scheduling.
While the world's most expensive goalkeeper deserved credit for a fine save, Arnautovic, who has scored three and assisted another of West Ham's five goals this season, would likely have converted one, or both, of Antonio's chances.
"Maybe in two, three or four months it will be a problem".
But with about 13 minutes to go West Ham had a wonderful chance to win the match, when the unmarked Yarmolenko headed just wide at the far post after a cross by Robert Snodgrass.
Hazard netted a fine hat-trick against Cardiff City in a 4-1 win last weekend in the Premier League, but Sarri elected to make a host of changes for the Blues' midweek European tie and a Willian strike handed them a 1-0 win to continue a fine start to the season.
Russia says OPEC, non-OPEC to discuss output scenarios in Algeria
It warned that prices could rise above $80 unless producers compensate for lost supply from OPEC members Iran and Venezuela. China, one of the world's largest oil consumers, on Tuesday added $60 billion of US products to its import tariff list.