Bournemouth nearly halved the deficit through Ryan Fraser - who curled the ball agonisingly wide of the far post from distance - but Chelsea were full value for their win and will be delighted with the start to their season heading into the worldwide break. This is a match Bourenmouth will be happy to take a point from.
"I think that now, for us it's better to think about the next match", he said.
"I think that he will be important for sure. If he improves that, he could be the best left-back in the world".
Sarri will breathe easily at the top of the table for another week, even if Chelsea's performances are yet to catch up with results.
Chelsea will be looking to maintain their 100% start to the new season when they take on Bournemouth at Stamford Bridge on Saturday afternoon.
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Bournemouth manager Eddie Howe: "We know how hard the game's going to be but we're very keen to keep the momentum from what has been a really positive beginning. He has great qualities from the physical and technical point of view, but he has to improve in the tactical point of view". "They defended very aggressively and the situation was not so easy".
He doubled up with Ake to keep Willian quiet and was a menace going forward, creating three chances - one of which should have ended in a goal from Wilson in the first half. But in this kind of match, usually you can win in the last 20-25 minutes. "I was really pleased to progress in the Carabao Cup".
Sarri's side appeared to be in danger of dropping their first points of the season against opponents who were also unbeaten coming into this game.
"Eddie came to Empoli four years ago for three or four days, and we stayed in Empoli together".
It was not until the 44th minute that Chelsea looked likely to find a way past Asmir Begovic, the former Blues keeper, when Marcos Alonso struck a right foot shot against the post from the edge of the penalty box.