The Gabon international, who opened the scoring in Saturday’s 1-1 draw at Crystal Palace, was booked for a tackle on Max Meyer but the video assistant referee upgraded the punishment to a red card.
Arsenal appealed against Aubameyang’s dismissal but the punishment stands.
The former Borussia Dortmund player, 30, has scored 14 of Arsenal’s 29 Premier League goals this season.
“Players have to step up,” Arteta said on Wednesday when asked if the team would miss their suspended captain.
“You know, when one of your big players is not there, they have to take responsibility. I’m sure when they’re not playing, they want a chance and they talk.
“It’s time to talk on the pitch, not outside. You come on there, you make the impact that he made and you show me that you are as good as him or even better. You have the chance.”
Arteta has also been hit by an injury to defender Sead Kolasinac.
The left-back is a doubt for Saturday’s Sheffield United game due to a thigh injury, with fellow left-back Kieran Tierney and right-back Calum Chambers both long-term absentees.
Arsenal have been linked with a move for Manchester City’s John Stones, with whom Arteta worked at the Etihad Stadium, but he said there would be no move for the England international.
“John is a player that I really like and I followed. We signed him when I was at Manchester City and I worked with him for many years and know him well,” he said.
“When I look at centre backs he has many attributes that I like from one, but we’re not interested.”
