"It is better to be on the pitch than watching on the bench, but the boys when they are playing they did well so I am just happy for the win", he said.
"I think we did really very well in the first 25 minutes today", Sarri told reporters.
"We did very well for 75 minutes of the 90".
Dixon said the Chelsea boss "might need a fag" after they surrendered a 2-0 lead to go in at half-time level. I still have two years of contract [left] and we'll see what happens.
In a tighter second half, neither side could carve out as many chances but Alonso settled the game when Belgium winger Eden Hazard, on as a substitute, carved open the Arsenal defence for the Spanish defender to finish in Sarri's first home game in charge.
"But we need to continue and press and press and press in the other half". But not in the other 15 minutes. "In the other 15, it was better to smoke, I think", he said. Otherwise it might be a problem.
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.
Sarri said he started the match with Hazard on the bench because he still seemed exhausted after helping take Belgium to the World Cup semi-finals in July.
"It would be a bit unusual for [Chelsea] to let me go and not recruit another player".
Hazard's contract runs until 2020 with Chelsea hopeful he will renew to end speculation over his future.
Plus ça change, plus c'est la même chose: the more things change, the more they stay the same.
"He is special, and it's encouraging for them; they've got the new players settling in quickly, and Mateo Kovacic coming in too, and then you've got Hazard who is just a class act". "I'm fine here. We'll see what happens in a year or two".