The club tried to sell the former Everton academy player in the last three windows — but found no takers.
But Arteta said: “I've worked with players like this, I've had team-mates like this and there is always a moment where they click.
“I can accept a mistake, no problem. What I'm not going to accept is someone who makes a mistake and then stops playing, doesn't want the ball and doesn't want to make decisions.
“That player is not acceptable for our team.
“But Musti, after that incident against Chelsea, tried to play every single time, he went for every single challenge, he put his body on the line.
“He was down afterwards, yes, but he reacted and if he does that, he will overcome the situation.
“I ask him to play the way we want to play, he made a mistake, on another day it will be someone else.
“We want to minimise them and find the reason why that happens but I like his reaction after that."
Arteta's predecessor Unai Emery revealed in August that Mustafi had been told he could leave.
But the centre-back has ended up outlasting Emery and now has a manager who believes in him.
Arteta added: “While he is my player and he is training with me the way he does of course he has a long-term future at Arsenal.
“The plans maybe in the summer were different with him, I came here, he is here and his attitude is right. He wants to help."
Yet Arteta warned Mustafi, 27, his problem is more than just confidence.
Pep Guardiola's former No 2 said: “Confidence is not the only issue. I don't believe that at nearly 28 you cannot improve certain aspects of the game.
“I believe that you can. It's my job to do that."