Neville's Inter Miami beat Rooney's DC United 3-2 on Sunday, but the result was overshadowed by an in-game delay.
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Taxiarchis Fountas of United was accused of racially abusing Inter defender Damion Lowe in the 59th minute of the match, leading to a four-minute stoppage in play.
The Greek forward took to Instagram to deny the allegations.
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"That despicable racial slur is one I denounce and did not use," the statement read. "We had a hot discussion on the field, but I have not racially abused anyone. I firmly reject racism in any form, it is despicable.
"I have many friends from many cultures. I always respect the culture, religion and skin color of each person, I am therefore very upset by this accusation and saddened to be falsely accused."
Former Manchester United teammates Neville and Rooney were summoned by referee Ismail Elfath, with the former striker substituting the accused player when play resumed.
Neville discussed whether his side should leave the field during the stoppage - and he praised Rooney, the players, and the referee for dealing with the situation.
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"There was a racist comment that was unacceptable," he said post-match.
"A word was used that I think is unacceptable in society. I think it's the worst word in the world.
"There is no place at all for racism on a football field or society.
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"I must commend my players for keeping their calm, I must commend the referee - a really difficult situation he followed the protocols set out by the MLS - and I must give massive, massive respect to Wayne Rooney for dealing with it in the way that he did.
"I have always known him as a class act and today he went up in my estimation more than he has ever done, more than any goal he has ever scored."
In the aftermath of the match an MLS spokesperson told ESPN: "MLS has zero tolerance for abusive and offensive language and we take these allegations very seriously. An investigation into this matter will begin promptly."
DC United also released a statement, saying: "DC United are aware of the allegations involving a player during the match against Inter Miami CF. The club will work closely with Major League Soccer and Inter Miami to investigate the incident."