The former Manchester United defender jokingly referred to his side's controversial win over the Gunners in October 2004.
United secured a 2-0 win at Old Trafford to end Arsenal's record-breaking Premier League unbeaten streak.
Mike Riley had been the referee that day, with Neville crossing paths with him again for a Sky Sports segment.
Neville and Jamie Carragher visited the Professional Game Match Officials Limited (PGMOL) to train with top flight officials.
Former referee Riley was the PGMOL general manager at the time, having held the role from 2009 to 2023.
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He also spent 13 seasons as a Premier League referee as well as officiating in the Football League, Europe and international matches.
After interviewing Riley, Neville stood up to shake his hand and quipped: "Thank you very much for that Arsenal Man United game all those years ago. It was wonderful that. Thanks very much."
The trio burst into laughter, but Arsenal fans have not seen the funny side after the video resurfaced on social media.
Reacting to the clip, one fan wrote: "Couldn't believe what I'd heard."
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Another commented: "This boils my blood."
Meanwhile, a third supporter asked: "How did they get away with this?"
The Red Devils ran out 2-0 winners to hand Arsenal their first league loss in 49 matches.
However, it was not without controversy after Ruud van Nistelrooy converted a contentious penalty to open the scoring.
Gunners fans also felt Rio Ferdinand should have been sent off for a challenge on Freddie Ljungberg.
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The match has gained notoriety for its heated nature and arguments over the refereeing decisions.
It has also become known as the 'Battle of the Buffet' after Cesc Fabregas threw pizza at Sir Alex Ferguson.
His antics came as tempers flared in the tunnel at full-time between players from both teams.