Manchester United say they are "disgusted" after Axel Tuanzebe and Anthony Martial were racially abused on social media by "mindless idiots" after Wednesday's loss to Sheffield United.
Both players started the 2-1 Premier League defeat at Old Trafford.
United midfielder Scott McTominay wrote on social media that he was "disgusted with what I have read this morning".
Club captain Harry Maguire added: "United against racism. We will not tolerate it."
Former United defender Rio Ferdinand called it a "disgrace", adding: "These ignorant idiots need to be exposed so everyone can see them for what they are."
In a statement, the club said: "Everyone at Manchester United is disgusted by the racial abuse received by players via social media after last night's game.
"We utterly condemn it and it is encouraging to see other fans condemn this on social media also.
"Identifying these anonymous mindless idiots remains problematic. We urge social media platforms and regulatory authorities to strengthen measures to prevent this kind of behaviour."
Anti-racism charity Kick it Out said the continued abuse of players on social media is "completely unacceptable" and reiterated its stance that those responsible for online hate must face "real-life consequences".
"We know that discriminatory abuse can have significant real world impact on the welfare of the victims," Kick it Out chairman Sanjay Bhandari said.
"We will continue to work with the football authorities, law enforcement and social media companies to try to rid football of hateful and discriminatory behaviour."
The Professional Footballers' Association (PFA), the players' union, has encouraged Tuanzebe and Martial - as well as any other player targeted by racial abuse - to "press charges".
"We want perpetrators to be held accountable for their online behaviour," the PFA said in a statement.
"The accounts of those sending the messages must be banned. Their details need to be provided to the appropriate authorities to take further action."