A red card was shown after VAR informed referee Paul Tierney a tackle by Aubameyang was dangerous, with the striker sliding in on Palace's Max Meyer after 65 minutes of Saturday's 1-1 Premier League draw at Selhurst Park.
According to BBC Sport, Arteta said he's disappointed to lose his captain for three games after the "completely accidental" challenge:
"It's a big shame and a big loss for us, but he mistimed the tackle and we have to accept it.
"It's an action that is completely accidental, in my opinion. He's been superb under me, he's working so hard. He's scoring goals and has probably been the most important player so to lose him is really bad news for us.
"Players have to step up. You know, when one of your big players is not there, they have to take responsibility."
There appeared to be no malice in the 30-year-old's red-card tackle, but the video replay showed the forward make forceful contact with Meyer's ankle.
Aubameyang apologised to Meyer via an Instagram post (h/t Goal), saying: "Hopefully Max Meyer gets well soon, I really didn't want to challenge him so hard and I appreciate that the boys fought hard to take that win, but unfortunately we come back with a draw. We keep going."
A statement from officials regarding the tackle stated a red card was issued as "the intensity of the challenge endangered the safety of the opponent," constituting "serious foul play," per Goal.
The forward has 16 goals for Arsenal in the Premier League and UEFA Europa League this season, and Arteta will now look to Alexandre Lacazette and Nicolas Pepe to supplement Aubameyang's regular contributions in the final third.