The 28-year-old Brazilian midfielder started for Ole Gunnar Solskjaer's men and was partially at fault for Liverpool's third goal on Thursday.
Fred was withdrawn in the 63rd minute for Mason Greenwood as United failed to mount a successful comeback against the Reds.
According to Sky Sports, the Brazil international was sent abuse on Instagram after United slipped to back-to-back Premier League defeats.
The targeted abuse was in the comment section of an image that Fred had posted on the social media platform on Sunday, which celebrated United's 3-1 win against Aston Villa.
Fred, who was signed from Ukrainian side Shakhtar Donetsk in 2018, has already been subjected to racial abuse this season after United's FA Cup exit to Leicester City in March.
The shocking messages included racial slurs and 'monkey emojis' after Leicester's 3-1 win at the King Power Stadium in the FA Cup quarter-finals.
Fred took to social media at the time and hit back at the racially abusive messages, saying that they "cannot feed that culture" and "cannot [accept] it."
The former Shakhtar star tweeted: "Social media comments filled with hate and, above all, racism: we cannot feed that culture.
"We cannot [accept] it. We have to fight it always. We are bigger and better than that. Enough!"
United players Marcus Rashford, Axel Tuanzebe and Anthony Martial and Red Devils women's player Lauren James have all been subjected to online racist abuse this season.
The Red Devils have previously revealed that there has been a staggering '350 per cent increase' in racial and homophobic abuse directed towards their players between 2019 and 2021.
United were among the many football clubs to recently participate in the social media blackout in response to the "sustained discriminatory abuse received online by players and others connected" in the sport.
Featured Image Credit: PA
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