The Duke of Cambridge has urged world football governing body Fifa to "show that it can represent the interests of fair play and put the sport first".
Prince William, the president of the FA, made his comments during a speech before the cup final at Wembley.
He urged sponsors and other backers to use their influence with Fifa to support reform.
It comes after Fifa's president Sepp Blatter was re-elected, following the arrests of seven people linked to Fifa.
The seven, arrested in Zurich earlier this week, are among 14 indicted on charges of bribery, racketeering and money-laundering, involving tens of millions of dollars since 1991.
'Huge disconnect'
Meanwhile, Swiss authorities have launched a separate criminal investigation into the awarding of the 2018 and 2022 World Cup tournaments to Russia and Qatar.
The prince led England's bid team for the 2018 finals, which also included Prime Minister David Cameron and David Beckham among others.
In his speech at Wembley he compared the crisis engulfing Fifa to the Salt Lake City corruption scandal, which occurred when the US city was bidding to host the 2002 Olympic Winter Games, and it prompted the International Olympic Committee to reform.
He said: "There seems to be a huge disconnect between the sense of fair play that guides those playing and supporting the game, and the allegations of corruption that have long lingered around the management of the sport internationally.
"The events in Zurich this week represent Fifa's Salt Lake City moment, when the International Olympic Committee (IOC) went through a similar period of serious allegations.
"Fifa, like the IOC, must now show that it can represent the interests of fair play and put the sport first.
"Those backing Fifa, such as sponsors and the regional confederations, must do their bit to press these reforms - we are doing football and its fans no favours if we do not.
"I have no doubt that when Fifa reforms, its mission to spread the benefits of the game to more people, especially those in developing countries, can only be enhanced."
He also used his speech before match - which saw Arsenal beat Aston Villa 4-0 - to back a decision by former Manchester United chief executive and newly-elected Fifa vice-president David Gill to quit the position almost immediately in protest at Mr Blatter's re-election.
Mr Blatter is not named in the indictment, and denies having anything to do with an alleged $10m (£6.5m) bribe.
Prince William said: "I know I join with all of you in commending David Gill for his decision to stand down from the ExCo [executive committee], and to lead by example by doing so."
And he said that the Football Association, the sport's governing body in England, had been "taking a critical look at itself under Greg Dyke's leadership" and could become the "gold standard of sporting governance".
The duke added: "We must ensure that the quality and the richness of the game at the highest levels is shared more generously at the grassroots; we must ensure that home-grown talent is better nurtured; and we must continue to kick out racism for good from our game.
"I feel we need to ensure that we become the gold standard of sporting governance. A modern, transparent and inclusive organisation - representative of the broad and diverse society who play and love our game.
"Over the next few years, if we want credibly to influence the debate on reform in Fifa, we must continue to strive for excellence in our own organisation.
"It's not easy to do so, but it is worth it - and, to that end, I commend the process you are on, and I'll be watching it closely."
Meanwhile, Football Association chairman Greg Dyke has said that England would back a European boycott of the 2018 World Cup.
A boycott will be considered by European football's governing body Uefa when it meets next week in Berlin.
Mr Dyke said: "There's no point boycotting on our own, but if the rest of Europe decided to boycott we would join them."
He also said England would not bid to host the World Cup under Blatter.
Writing in the Sunday Times, Culture Secretary John Whittingdale said "no option should be ruled out" in the fight against corruption - including a World Cup boycott.
He added: "If any evidence of criminal wrongdoing in the UK emerges, we will expect the police and CPS to pursue it with the full force of the law."
(BBC)