Rice, who was a key player for England at the Euros, said ahead of July's Wembley final that "we will be ready for it 10 times harder than they (Italy) will".
Bonucci admits Rice's words had reached Italy's players before kickoff.
He told the Athletic: "We didn't pay much attention to it (It's Coming Home) until the Spain game.
"Then the anger inside of us began to mount. We wanted to show them that the final hadn't already been decided. That they hadn't already won.
"Hearing that song on repeat and the comment from Declan Rice saying England were 10 times more motivated to win than us… well, they're the kind of mistakes young players make.
"You don't say that. You should never say you want something more than somebody else or you're better than somebody else."
Need a VPN? Or seeking to switch? Then support Tribal Football by clicking here to sign up with our official partners NordVPN. Not only will you receive the best VPN experience, but also great discounts by signing up via Tribal Football. Thanks for your support!