Bibi received a red card in the 51st minute after the video assistant referee saw the shot.
“I disappointed my team at a crucial time in the game, and there are no excuses for my behavior,” the 25-year-old Ivory Coast player wrote on Instagram.
“I feel very sorry and would like to apologize to the fans, my colleagues, my coaches and everyone else in the club,” he added.
Bibi and Alyoski were subjected to racist abuse on social media after the match, and Arsenal and Leeds announced that they would work with local authorities to prosecute those responsible.
Pepe will miss Arsenal’s next three league matches, but he can participate in the Europa League next Thursday.