The visitors enjoyed 72 percent of possession at the London Stadium but failed to break down a determined West Ham side, who created enough clear-cut chances to win the game themselves.
Sarri said West Ham, who beat Everton last week after losing their first four league games of the season, had been tough opponents, adding that his team needed to find a way to move the ball more quickly.
Turning his thoughts to Saturday’s match against Liverpool at Stamford Bridge, Sarri, in his first season in the job, said it would be tough to compete with a side that had been developing for three years under Jurgen Klopp.
“They are a step forward than us in this moment,” he said. “We have started to work all together 35, 40 days ago.
“So for us, I think it’s a bit early. We have to work. We need to improve and then maybe in one year we will be at the same level of Liverpool.”
The Chelsea boss said he was unsure how many changes he would make for the midweek third-round League Cup tie, also against Liverpool.
Olivier Giroud won his battle with Alvaro Morata for a starting spot up front for Chelsea, keeping his place for the second Premier League match in succession.
But Marko Arnautovic, West Ham’s leading goalscorer this season, missed out after failing to recover from an injury he sustained in the victory against Everton last week.
Despite Chelsea’s control, the home side could have taken a lead against the run of play just before the half hour.
Felipe Anderson was quick to seize on a loose ball and played in Michail Antonio, who blasted over with his left foot.
That chance breathed new life into the home crowd and the players and Antonio drew a smart save from Kepa Arrizabalaga in the West Ham goal just two minutes later after a fine run from Andriy Yarmolenko.
N’Golo Kante nearly gave Chelsea the lead with a headed effort but the sides were goalless at the break.
The match fell into a similar pattern in the second half, with Chelsea dominating possession, but Giroud — picked for his more physical threat — struggled to make an impression.
The French World Cup winner was replaced 20 minutes into the second half by Morata, who went close to breaking the deadlock moments after coming on only to see Lukasz Fabianski pull off a stunning stop from close range.
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.
Fabianski pulled off another fine save as the clock ticked into injury time, diving to his left to deny substitute Ross Barkley and Willian blazed wide as Chelsea applied intense late pressure.
West Ham manager Manuel Pellegrini, who has managed to stop the rot with four points from the past two matches, said his side had to make their chances count.
“When you have such clear chances against big teams you must score one of them,” he said.
“And we had three clear chances before they created one chance but you must score.”