Aubameyang has not travelled with the squad for Thursday's Europa League dead-rubber against Dundalk.
Arsenal are already through to the knockout stages and assured of top spot in Group B having won their opening five matches of the campaign.
But it is domestically where Arteta is struggling to find a solution to a poor run of form and a run of lacklustre performances.
Arsenal sit 15th in the Premier League table after their sixth loss in 11 games this season came at the hands of north London rivals Tottenham last Sunday.
One of the main problems has been a lack of goals, only the current bottom three have scored fewer than Arsenal's 10 so far, with Aubameyang not scoring from open play in the league since the opening weekend.
Arteta said he was not tempted to take his skipper to Dundalk in an attempt to play him into form and that his recent blip does not mean he has an automatic place in his Premier League XI.
"No one is undroppable at the end of the day," he said.
"You have to find the right players to win football matches but we cannot forget what Auba has done for this club and what he's done in recent months – not years ago.
"And as well because I see how he is training, how he is behaving and how much he wants to turn the situation around.
"When I see that type of hunger I stay as a strong supporter to a player when he is established in the team and the performances that he has provided.
"Listen, today and this week, the response I have seen from the players and the reaction I saw from the players after the match, I cannot be any prouder.
"Auba was one of the main guys there and today he was walking the place with an energy that wouldn't be associated to a team or a player that is suffering at the moment and this is for me the way we have to approach it."
Asked if Aubameyang was the type of captain to cajole his team-mates and be vocal with his opinions, Arteta added: "If necessary he would do it but I think he transmits his energy, his desire and his commitment to the team in different ways."
While Aubameyang is likely to return to the team for Sunday's visit of Burnley, one man who will not be involved is midfielder Thomas Partey.
The Ghana international, a deadline day signing from Atletico Madrid, limped off during the loss to Spurs.
It was his first game back since missing the previous four with a thigh problem, but he pulled up just before Harry Kane made it 2-0 at the Tottenham Hotspur Stadium.
His inclusion had been touch and go up until the day of the game but Arteta insists he was not rushed back as he confirmed Partey is now expected to miss "a few matches".
"He got injured in the same area.
"Not exactly the same spot, but similar as it was before. We gave him an MRI yesterday. There was an injury there and he will miss the next few matches.
"He did incredibly well. He was very confident. We tested him three times. He had zero symptoms about it.
"But in football you have a lot of unpredictable actions and he went into the floor, his knee got stuck. After he needs to stretch and get up."