But the Italian is still under enormous pressure ahead of Chelsea's meeting with Manchester City in the EFL Cup final on Sunday.
Sarri said it was unusual his side were getting so much criticism compared to Arsenal, who have the same number of points in the Premier League and also reached the last 16 in the Europa League.
"I keep hearing people praise Arsenal's season, but they are not in the EFL Cup final, they have the same points as us in the Premier League and reached the last 16 of the Europa League just like us," he told Sky Sport Italia.
"I don't understand why people act as if our season is so negative and Arsenal's is impressive.
"It's true there have been many ups and downs, including some deep lows, but considering it's my first season in a new league and environment, I think that's acceptable.
"I did take over a team that finished fifth, not one that won the championship."
Second-half goals from Olivier Giroud, Ross Barkley and Callum Hudson-Odoi saw Chelsea cruise past Malmo, but Jorginho was booed by fans when he came on in the 76th minute.
However, Sarri defended the Italy midfielder, saying his side's start highlighted how much they needed the 27-year-old.
"I think in the first 30 minutes we understood why Jorginho is very important for our team," he said.
"We were in trouble to exit from our half, on pressing. With Jorginho, it's easier I think.
"I hope that our fans will be able to understand that Jorginho, for us, is really a very important player."