The Gunners are out of the Europa League at the semi final stage, drawing 0-0 with Villarreal at home and going out 2-1 on aggregate.
The result means Arsenal will be without European football next season for the first time since the 1995-1996 campaign.
Arsenal are ninth in the Premier League, out of all the domestic cups, and now out of the Europa League as well.
When asked post-game by reporters if he was still up for the job, Arteta said: "Yes."
He went on to say: "I wouldn't be sitting here if I didn't [think I could].
"You will see it. It is not about talking, it is about showing it on the pitch."