The duo received racist messages on Instagram after Ole Gunnar Solskjaer's side were beaten by the Blades at Old Trafford on Wednesday night.
Manchester United have called for social media companies to enforce stricter regulations after “anonymous mindless idiots” racially abused Axel Tuanzebe and Anthony Martial following the Red Devils' 2-1 loss to Sheffield United on Wednesday.
Kean Bryan opened the scoring at Old Trafford after some questionable goalkeeping from David de Gea, while former Blades defender Harry Maguire responded as he scored his first goal at the Theatre of Dreams to restore parity.
Chris Wilder's decision to bring on Oliver Burke in the second half paid off, however, with the striker having found a late winner via a deflection off Tuanzebe.
Both Martial and the centre-back were subjected to racist language and symbols in the wake of the defeat, with United having released a statement condemning the discrimination whilst calling for social apps to better police their platforms.
"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."
Former United captain Rio Ferdinand also weighed in on the subject, calling for the perpetrators to be outed in public and answer for their hate speech.
"This is a disgrace," the ex-Red Devils centre-back wrote. "These ignorant idiots need to be exposed so everyone can see them for what they are!"
The likes of Harry Maguire, Scott McTominay, Marcus Rashford and Brandon Williams also posted on social media to back the fight against racism in football and support their team-mates.
Anti-racism group Kick It Out also condemned the abuse, with chair Sanjay Bhandari releasing the following statement via Sky Sports: "We are disappointed that players are continuing to be subject to racist abuse on their social platforms, it is completely unacceptable