Pedro put the Blues ahead after nine minutes at Stamford Bridge before Alvaro Morata doubled the lead with a smart finish in the 20th minute.
Although the game was ultimately settled by Marcos Alonso's 81st-minute winner, Sarri had reservations about his side's performance.
Asked by Sky Sports News after the game if he saw Chelsea as potential title challengers, Sarri replied: "Not in this moment. We did very well in the last 25 minutes today, but I think that we have to work, we have to improve in the defensive parts, and I am not talking about only the defenders.
"The defensive phase of all the team, all players. Because if we press very high, we are able to do well. But in the moment where we are not going to press in the other half, we are in trouble. So I think we have to work and need to improve.
"I think we have done very well for 75 minutes. 15 minutes from maybe the 30th minute was horrible. We lost the distances I think, we were not able to cover the last third, or press as a team, only one player to player.
"I think that the players were very good in the second half. It was not easy in the final part of the first half. We want to defend by looking only at the ball. We have to stay very compact and need to press on the other half. In that 15 minutes, we were not able to do this, so we were in trouble.
"We have to improve because I think we did really very well in the first 25 minutes today, but we need to continue to press and press and press in the other half. Otherwise, for us it may be a problem. I hope we will be able to play 90 minutes like the first 25 in two months."
Chelsea sit atop the fledgling Premier League table with two wins from their opening two games.