Ole Gunnar Solskjaer’s side missed the chance to take top spot in the league when they fell to the division’s bottom club at Old Trafford.
Harry Maguire cancelled out Kean Bryan’s opener for the Blades but Oliver Burke’s 74th minute strike deflected off Tuanzebe to give Chris Wilder’s men only their second victory in the league this season.
Martial and Tuanzebe were targeted after the game, with some unprintable words left on their respective social media accounts by some perpetrators.
United have come out to condemn these actions and have called on social media companies to do more in clamping down on the menace.
"Everyone at Manchester United is disgusted by the racial abuse received by players via social media after last night’s game," a statement read.
"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."
