The Gunners suffered their third consecutive Premier League loss on Sunday after being beaten 2-1 by Wolves at home.
They are now in 14th place with 13 points in their first 10 games, and far from the pace for a European qualifying place.
But Arteta downplayed any talk he was worried about his job, insisting that his goal has only ever been to make his players perform to the best of their ability.
“It’s something that the day I decide to become a coach, I know that one day I will be sacked or leave the football club,” said the Spaniard.
“I don’t know if it’s the day after signing my contact, in a month, a year or six months. I never worry.
“My only concern is to get the most out of the players, to give the club the best possible service and to get better and better.
“I know, I repeat, in this profession, one day I will be made redundant or leave but I do not know when that will happen.
When asked if he was concerned about his team’s recent poor performance, Arteta admitted: “It’s when you lose three games in a row for different reasons at home. I am really worried, I am responsible for it.
Reflecting on the loss to Wolves, Arteta said: “A very bad result. The performance, in the first half, we had our moments, they had two shots on target and they scored twice.
“We had a very good reaction in the second half, we did everything for. I think the team showed a desire, how badly they wanted to win the game.
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“We created opportunities, we created opportunities and the goal didn’t arrive. Visibly disappointed because I think we deserve more from the game.
“It’s (a concern) when you lose three games in a row for different reasons at home.
“Obviously I’m really concerned, I’m responsible for it, but I have the reaction of the team, the way we played the second half.
“I expect more quality and more capabilities from them, but in the end, the desire and the will to achieve a result was there.