Pepe was sent off after 51 minutes following a clash with Alioski as the pair tangled off the ball repeatedly before the Arsenal winger headbutted the Leeds defender.
Referee Anthony Taylor was alerted to the incident by VAR and showed Pepe a red card for violent conduct after consulting the pitchside monitor, which will rule him out of Arsenal's next three domestic matches against Wolves, Tottenham and Burnley.
But the incident has been overshadowed by sickening abuse aimed at the pair with several ex-players including Phoenix Rising winger Shaun Wright-Phillips urging Twitter to take action.
Alioski has also been subjected to racist abuse and sources have told ESPN that his family has been threatened.
Both Arsenal and Leeds vowed to work with the relevant bodies to identify the individuals involved.
"We utterly condemn the vile abuse directed at Nicolas Pepe and Ezgjan Alioski on social media following our match against Leeds United," Arsenal said in a statement on Monday.
"This is completely unacceptable and we will be working with the police and authorities to do everything we can to trace and prosecute the culprits."
A Leeds statement read: "The vile abuse directed at Ezgjan Alioski and Nicolas Pepe on social media after yesterday's Premier League game with Arsenal will not be tolerated by Leeds United.
"We will work closely with the police and the footballing authorities to ensure those responsible are identified and punished."