The Arsenal captain has scored just two Premier League goals all season and was a peripheral figure once again as they slumped to a 2-0 defeat in Sunday's north London derby at Tottenham Hotspur.
Aubameyang is not expected to feature in Arsenal's final Europa League Group B match at Dundalk on Thursday night given they have already secured top spot but when asked whether he would keep playing the 31-year-old in the League no matter what, Arteta replied: "No one is undroppable at the end of the day.
"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. 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.
"I know how difficult it is for everybody at the moment after losing the derby you can be completely down and I saw a completely different team that wants to fight, that is united, that has a big belief in what they are trying to do and they want to do it themselves and push each other harder and harder.
"Auba was one of the main guys there and today he was walking [around] 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."
Arteta also confirmed Thomas Partey will be sidelined for "the next few matches" after suffering a thigh injury at Tottenham.
Partey was originally expected to miss the game with a similar problem sustained against Aston Villa on Nov. 8 but pushed to return to action, only to limp off before half-time in the build-up before Spurs scored their second goal.
Arteta provided an update while defending his decision to play the midfielder at the Tottenham Hotspur Stadium.
"He got injured in the same area," Arteta said. "Not exactly the same spot, but similar as it was before.
"We MRI [scanned] him 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. Immediately he put a lot of stress in a similar area and he felt it again.
"After it was said it was a bit too early [to play Partey]. I don't think it was because he was completely fine to play."