The players, who started the fixture for Ole Gunnar Solskjaer's side, were targeted on Instagram, with a number of racist comments and symbols appearing on old photos.
Club captain Harry Maguire responded on Thursday morning, posting a photo of himself taking the knee prior to kick-off.
"UNITED against racism. We will not tolerate it," he wrote on Twitter.
On Instagram, Scott McTominay also offered his support to Tuanzebe. “My brother. Disgusted with what I have read this morning,” he wrote.
A statement released by Manchester United read: "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.
"Manchester United has zero tolerance of any form of racism or discrimination and a long-standing commitment to campaigning against it through our All Red All Equal initiative. Identifying these anonymous mindless idiots remains problematic.
"We urge social media platforms and regulatory authorities to strengthen measures to prevent this kind of behaviour".
Sanjay Bhandari, chairman of Kick It Out, said: "We are disappointed that players are continuing to be subject to racist abuse on their social platforms, it is completely unacceptable. We will continue to work with the football authorities, law enforcement and social media companies to try and rid football of hateful and discriminatory behaviour.
"As we have said before, online hate must have real-life consequences, so people don't continue to spread hate as freely as they wish. The individuals responsible for this abuse will hopefully be identified by the social media platforms and swiftly removed. We know that discriminatory abuse can have significant real world impact on the welfare of the victims.
"We encourage the players to get such support from their club in the first instance, and support is also available from the PFA and Kick It Out.”
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