Having beaten Huddersfield in their season-opener, the Blues prevailed 3-2 at Stamford Bridge to make it back-to-back top-flight victories at the start of Sarri's tenure.
Marcos Alonso's late strike proved decisive after Arsenal had fought back from two goals down, but Sarri tempered any talk of challenging for the championship by suggesting he still had plenty of work to do.
"No, not in this moment," he said when asked if his side were among the favourites. "We did very well in the last 25 minutes, but I think we have to work.
"We have to improve in the defensive phase and I'm not talking about only the defenders. The defensive phase of all the team, all the players.
"If we press very high, we are able to do well. But, at the other moments, when we are not able to press in the other half, we are in trouble. So I think we have to work and we need to improve."
Eden Hazard again started on the bench for Chelsea as he continues his return to fitness following an extended break after the World Cup.
The Belgium star replaced Willian just after the hour, going on to set up the winner with a brilliant cutback into Alonso's path.
"It's clear. He is a great player," added Sarri.
"But I think that, at this moment, he's not able to play for 90 minutes, so I thought it was better to give him 25-30 minutes when the intensity of the match has come down.
"But I think, I hope, that in one week, maximum two weeks, he'll be able to play the whole game."
Chelsea head to Newcastle next weekend.