The three royals joined the former England rugby ace, 44, who is married to The Princess Royal’s daughter, Zara, on his show The Good, The Bad and The Rugby, alongside co-hosts James Haskell and Alex Payne.
During the discussed at Windsor Castle, father-of-three William, 41, revealed the ‘only time I’ve ever cried when watching sport’.
He admitted that he’d shed a tear when watching his cousin, Zara, 42, compete, saying: ‘The only time I’ve ever cried when watching sport was when Zara won I think it was the European championship.
‘I was down in Exmore at the time camping. We were all huddling around the phone watching it. She was there she was blubbing away the flag was going up. I was in pieces.’
Kate added: ‘I can remember because you came back and said I’ve never been so proud of anyone.’
Elsewhere, Princess Anne recalled the early days of her daughter’s equestrian career, in which she won a silver medal at the 2012 Olympics.
Recalling what would happen if she tried to offer her advice, keen horse rider Anne said: ‘If I made a comment I was usually told I was a dinosaur.’
William, meanwhile, recalled the 2012 London Olympics and the ‘coming together of a nation’.
He said: ‘It was phenomenal and I think Chris Hoy at the velodrome was one of my all-time favourite moments – we were both there shouting and yelling – it was this cauldron of noise and it was just so exciting.’
The prince continued: ‘The Paralympics particularly, that was a huge moment for disability sport taking off and it obviously got bigger and bigger since then.’
Kate commented: ‘In 2012 I was absolutely gutted to miss Andy Murray’s game when he won his gold medal against Federer.’
The Prince and Princess of Wales’ appearance on the podcast comes ahead of their journeys to France this weekend to watch the Rugby World Cup.
Meanwhile, William, who is patron of the Welsh Rugby Union, will watch Wales play Fiji at the Stade de Bordeaux on Sunday.
It comes weeks after the Prince, who is president of the Football Association and therefore responsible for promoting the game nationally and internationally, chose not to attend the World Cup final which saw England play Spain in Australia.
The cost of the trip and carbon footprint were cited as reasons for him not to go.
Palace sources said it might be considered tactless for William to return for the first time in almost a decade to publicly cheer England on in the finals they put Australia out of the tournament to get there.
A source told the Mail: ‘It was a finely balanced decision. The Prince of Wales hasn’t visited since 2014, so he would wish his next trip to Australia to be a substantial visit.
‘He met them [the Lionesses] in St George’s Park before they flew out and he has been supporting them throughout the tournament by sending private good luck messages to the manager and team.’
But critics rounded on the Prince, as the Government frantically scrambled Foreign Secretary James Cleverly to Sydney to support Sarina Wiegman’s side.
Mandu Reid, leader of the Women’s Equality Party, told MailOnline: ‘It’s utterly ridiculous that England wasn’t and still isn’t prepared to celebrate the women’s World Cup final.
‘The President of the Football Association, Prince William, isn’t bothering to attend, licensing laws haven’t been relaxed, there won’t be a screen at Trafalgar Square, and there’s been no word of any kind of large celebration should they win.
‘This last-minute scramble to show support for the Lionesses by our leaders isn’t just embarrassing, it reveals how little they think of women’s sport.
‘You can guarantee that there’s no way the men’s football team would be treated with such disregard and disrespect.’
Prime Minister Rishi Sunak was also absent, due to ‘existing Government business commitments’, but cheered the Lionesses on from Yorkshire, a source said.
Labour MP Kate Osborne told Times Radio: ‘We all know that if this was the men’s final, Sunak, and the FA president, Prince William, would be in attendance no matter how long the flight to Australia is.’
Gerry Sutcliffe, who served as sports minister under Gordon Brown between 2007 and 2010, told the Telegraph: ‘I think the Prince of Wales should be there.
‘I know it’s a long way and I’m sure he has family commitments, but this is a unique moment, it’s the World Cup final.’
Neither William nor Mr Sunak attended any of the England men’s World Cup games in Qatar last winter.
However, the row was intensified when Queen Letizia and her 16-year-old daughter, Infanta Sofia, went to Sydney ‘to show, once again, the royal household’s support for national football’.
The pair sat in the presidential box at the Accor Stadium, but weren’t joined by King Felipe, who was busy with other official duties.
Letizia visited the Spanish team in Madrid before they travelled to the tournament, watching them train and being presented with a personalised jersey.
She ended the visit with ‘a motivational speech that resonated deeply with the players and coaching staff’, the federation said.
FA chief executive Mark Bullingham said that bosses had always known William would not be attending, but that he had been a ‘brilliant supporter of the team throughout’.
Before the final, in a video posted on the Prince and Princess of Wales’s social media account, Prince William wished the Lionesses luck alongside his daughter Princess Charlotte, who held a football.
William said: ‘Lionesses, I want to send you a huge good luck for tomorrow.
‘We’re sorry we can’t be there in person but we’re so proud of everything you have achieved and the millions you’ve inspired here and around the world. So go out there tomorrow and really enjoy yourselves.’
A beaming Charlotte, dressed in shorts and a T-shirt, added: ‘Good luck Lionesses!’
The decision for the couple to attend the matches in France comes after they enjoyed a summer break in Balmoral with the Royal Family.