The Madness frontman - whose group performed on the roof of the royal residence - was left red-faced when he went to speak to the royal and Black Eyed Peas star will.i.am, only for them to walk away as he approached.
Suggs told Absolute Radio: ''It was the Bow Room, which was the after show party, and it was full of princes and princesses. Our keyboard player, Mike, had a meltdown standing between Stevie Wonder and Paul McCartney and Prince William, 'What we doing here? We shouldn't be here!'
''Everyone basically in the room was elbowing everyone else to go and say hello to someone who was being elbowed to go and say hello to someone else, but my daughters made me go and say hello.
''Will.i.am was talking to William, right, and you've got to say that he's irresistible. Of course, I bowl up to Will.i.am and William, they both stroll off in opposite directions, leaving me standing on my own. I looked back to see my daughters have run away.''
Despite Suggs' embarrassment, the group found the show a ''wonderful'' experience, but admitted it was slightly bizarre.
Suggs' bandmate Chas Smash added: ''It was surreal. Unique. Strange. Odd. Brilliant. Wonderful. Best view of London I've ever had though, you could see everything, you know, the Eye, Parliament, Post Office Tower, it was fantastic.''