The Gunners are yet to win or score any goal in their first two Premier League matches this season.
Romelu Lukaku and Reece James both scored in the first half to secure all the points for the Blues on Sunday.
In their first game of the season at the Emirates, Arsenal fans booed the players at halftime as well as at full-time.
Some of them then vented their anger directly at Arteta as he made his way home on Sunday evening.
As Arteta’s car was stationary, several fans gathered around the driver’s window and urged the Spaniard to resign.
One supporter could be heard asking: “Arteta, was that good enough? Please leave the club.”
Another man said: “Arteta, do yourself a favour. Mikel, do yourself a favour, please leave.”