'Pedro for us is very important, because he is the best player we have with movement without the ball, ' Sarri said.
Indeed, the majority of the game's best chances fell to the home side, with Felipe Anderson and Andriy Yarmolenko both looking lively on the flanks.
"It's impossible to win every match", he added.
Things are not about to get much easier for the Blues, who face Liverpool in an EFL Cup and Premier League double-header in the next week. With their confidence higher following a rare win at Everton last Sunday, the Hammers rarely looked troubled by their West London neighbours during the first hour.
Top scorer in the Premier League with five goals and a couple of assists to his name, scorer of a hat-trick last time out against Cardiff, all the talk pre-match was about how West Ham would have to contain Chelsea's No 10 to take anything away from the game. "So for us it's a bit early", Sarri said.
The match fell into a similar pattern in the second half, Chelsea searching for openings around the West Ham box but Felipe Anderson and Yarmolenko looked unsafe when the home side broke forward. Then, I think that we have played very well. well in the second half, generally, but very well in the last 25 minutes.
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While he shouldn't be unhappy about the entirety of his performance, Hazard will at least feel a deep dissatisfaction at he and his team's ideal start to the season being stifled and checked at the London Stadium.
The Frenchman 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.
'We need to move the ball quicker, I think. They had one clear chance that (Alvaro) Morata's missed after the rebound.
Creativity was not one of Chelsea's strong points against West Ham's deep defence, as they struggled to find a way through consistently.