The 24-year-old royal reportedly made the comment to Holden at a recent Palace event.
"Prince Harry came over and said to me, 'Is Piers Morgan really a prat?' I said, 'You can't say that, but yes!'" she told Heat.
"He even told me he records Britain's Got Talent every week on Sky Plus!"
The 38-year-old went on to reveal that Prince Charles had also been watching the hit ITV1 show.
"Charles came over to me and said, 'Oh, you do the show with the buzzers, don't you?' I said, 'Yes. I didn't even know you watched telly! If you came on our show, what would you do? Can you juggle?'
"And Charles replied, 'Oh no, no I can't do anything'. To which Camilla added, 'Yes, I can vouch for that - he's not that talented'."
Dance group Diversity were crowned champions in this year's series and will perform for the Queen at the Royal Variety Performance.