The Gunners excelled under Arteta last season, winning the FA Cup, but they have made a stuttering start to the current campaign.
As a result, Arsenal are 13th in the table and Arteta was asked whether he now fears for his job.
“It’s something that the day I decided to be a coach I know that one day I will be sacked or leave the football club,” he said.
“I don’t know if it’s the day after I sign my contact, in a month’s time, a year’s time or six months’ time. I never worry about it.
“My only concern is to get the best out of the players, give the best possible service to the club and become better and better. I know, I repeat, in this profession, one day I will get the sack or leave but I don’t know when that is going to happen.”
Arsenal’s defeat to Wolves was the visitors' first win at the Gunners in the League since 1979, but their victory was tainted somewhat following a serious injury to Raul Jimenez.
The striker clashed heads with David Luiz in the fifth minute and was taken to hospital to undergo further medical treatment.
Luiz, however, was bandaged up and played the rest of the first-half before coming off at the break.
But Arteta said: “The doctor made all the tests and followed all the protocols.
“He responded well to all of them but it was a nasty cut. David wanted to continue but at half-time we took him out because he was not comfortable heading the ball.”
Luiz will now be a doubt for Arsenal’s next match, against Rapid Vienna on Thursday, and they will be without Thomas Partey too.
The midfielder joined in the summer for £45million, but he is struggling to get fit after injuring his thigh against Aston Villa at the start of November.
“I don’t think he will be with us in the next few games,” said Arteta.
“We have been missing a lot of players. We have many, many different issues, but I don’t like to use that excuse.
“At the end of the day, we are all the time really close to winning football matches and we end up losing it in the last few games. This is only in our hands with the players that we have. It is what we have to do. We cannot change that. It is in our hands.”