Chelsea’s early domination saw them go 2-0 up thanks to goals from Pedro Rodriguez and Alvaro Morata.
Arsenal however fought back to level the score through Henrikh Mkhitaryan and Alex Iwobi before Marcos Alonso scored the winner for Chelsea late in the game.
Reacting to the win, Sarri posited that his side must improve defensively to have any hopes of topping the table in May.
He said: “We are not title challengers, not in this moment.
“We have to improve in the defensive phase and I’m not talking about only the defenders.
“We did very well for 75 minutes — 15 minutes at the end of the first half was horrible.”