Declan Rice's pre-match comments combined with fans continuously singing 'football's coming home' played into Italy's hands, Bonucci has claimed.
"We wanted to show them that the final hadn't already been decided. That they hadn't already won, he said.
"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."
Before the game, Rice told talkSPORT he and his teammates were relishing the battle against their experienced opponents.
"I can assure you, we will be ready for it 10 times harder than they will. We are ready to run, ready to go to places we've never been before," he said.
"This is life on the line stuff now. This is the chance to make history. There's no way we are not going to go out there and give it everything.
"The midfield battle will be key, but all over the pitch it will be key as well. We will be ready."
However, the Three Lions lost on penalties and their wait for a first major tournament win since the 1966 World Cup goes on.
Bonucci's ecstatic celebrations in the summer mirrored Croatia's delight at winning their 2018 World Cup semi-final against England.
The song - Three Lions - is often mistaken for English arrogance by our friends overseas when it's the opposite.
"You should always put yourself on the same level as your opponent, keep a low profile and strike at the right moment," Bonucci added.
"That's what we did. We never said we were going to win, just that we were an inch away from going all the way and getting the right result.
"We were never presumptuous about it. We stayed humble and that's what made the difference.
"We had a great team, a great coach and a great staff behind us. To give our country and ourselves that kind of joy was something truly special."