Tweets referring to Young as an 'ape' and using the 'n'-word were flagged up by football equality charity Kick It Out after the 33-year-old endured a disappointing night in United's 3-0 defeat in Barcelona.
Kick It Out has now demanded Twitter do more to tackle racism after a string of recent high-profile incidents on the social media site, including abuse aimed at England international Raheem Sterling and Liverpool forward Mohamed Salah among others.
In a statement, Kick It Out said: 'Yet another black player, this time Ashley Young, targeted with racist abuse on social media after tonight's Champions League game.
'Again, we're left asking Twitter the same question - when will you take serious action to tackle the rampant discrimination on your platform?'
When contacted by Sportsmail, a spokesperson from the social media website said: 'While we welcome people to express themselves freely on Twitter, we do not tolerate behaviour that crosses the line into abuse, hateful conduct or harassment. Abuse and harassment - no matter who the victim - have no place on Twitter.'
Twitter condemned the abuse of Young but did not say whether they would be taking individual action against users who sent the footballer racist abuse - 'we can't comment on individual cases for privacy and security reasons.'
The offensive tweets have now been removed from the site, and several of the users who abused Young appear to have deleted their accounts.
