The Gunners lost for the fifth time in the league this season after Pedro Neto and Daniel Podence’s first half goals rendered Gabriel Magalhaes’ equaliser a mere consolation in the end.
Arteta’s side dropped to 14th on the league table and are winless in the league since a 1-0 victory over Manchester United at Old Trafford at the start of November.
The loss to Nuno Esperito Santo’s men means Arsenal have lost their last three league games at home, with Leicester City and Aston Villa all taking three points away from the Emirates stadium.
Arsenal have scored just 10 goals in their 10 games and as the pressure starts to mount on Arteta, the Spaniard insists he is not scared of getting the sack.
"The day I decided to be a coach, I know that one day I will be sacked, or I will leave the football club,” Arteta said post-match.
"I don't know if that was the day after I signed my contract, in a month's time in a year's time or six months - so I never worry about it.
"My only concern is to get the best out of the players, get the best possible service to the club and become better and better.
"I know, I repeat to you, in this profession one day, I will get the sack or I will leave, but I don't know when that's gonna happen.
"We have to improve, it is clear it is not near good enough for this football club, and we have to change this dramatically."
It does not get any easier for Arteta and his boys as they make the short journey to table-topping Tottenham Hotspurs in their next league outing.