The club is working to identify social media users who have racially abused the advocate
Manchester United will take "the strongest possible action" against individuals who have made racist comments about Ashley Young on social networks.
Discriminatory left-back and side-by-side appearances as fans of United came on Twitter after the quarter-final defeat of the Champions League to Barcelona on Tuesday.
England's young international played the whole game when Ole Gunnar Solskjaer's side fell to a 3-0 defeat, ending their campaign in Europe.
"Manchester United totally condemns the racist social media comments posted around yesterday's Champions League event," a club spokesman said on Wednesday.
"We are working to identify the individuals involved and will take the strongest action possible against them.
"There is no place for racism within our game, or in society as a whole, and we are committed to working to make football free from all forms of discrimination."
Anti-discriminatory group Kick It Out has issued a statement on Twitter demanding that the social media platform be stronger in eliminating abuse.
A post on the organization's account said: "Yet another black player, this time Ashley Young, has been the target of racist abuse on social networks following tonight's Champions League game.
"Again, we are asking the UK's Twitter the same question – when will you take serious action to combat unbridled discrimination on your platform?"
Meanwhile, Twitter added, "We do not comment on individual cases for privacy reasons.
"Our abusive behavior policy prohibits behavior that attempts to harass, intimidate or silence another person's voice, and we take strict enforcement measures if violations are found.
"Progress in this space is difficult, but we are deeply committed to improving the health of the talk on the platform.
"To this end, we are now suspending three times more abusive accounts within 24 hours of receiving a report than last year. We will continue to develop this work to prioritize the security of our users."
Young, 33, is United's captain in the constant absence of Antonio Valencia in the teams of the round.
The defender made 25 appearances in the Premier League for the club this season, in addition to seven times in the Champions League.
The club's next game is against Everton in the Premier League on Sunday, as the Red Devils want to continue the race for a