Luis Fabiano was the star for the South Americans, scoring twice to set them on their way, before an own goal from Andrea Dossena in first-half injury time made it three goals in a remarkable seven-minute spell.
The world champions improved in the second half, but not enough to score the one goal they required to take the final semi-final spot, which went to USA courtesy of their 3-0 triumph over Egypt.
"We came into this game with very good concentration because we knew we were going to play a very good team with a lot of quality," the former Arsenal midfielder said. "We tried from the beginning not to give them space, especially the midfield players, who have a lot of quality to put balls forward for their strikers.
"From then on, we got the ball and the speed going forward was crucial. Our counter attacks were decisive to scoring the goals. It was important for us to win, but the way we played was really good, especially the three goals in the first half. That gave us more room to relax in the second half. I think the way the team played was very good."
Gilberto, who now plays for Panathinaikos in Greece, also felt that the players being together in the national set-up for a month - they came together prior to a FIFA World Cup™ qualifier against Uruguay in early June - was aiding their progress. He continued: "We're getting better and better with each game. The team has now been together for almost a month, since the game against Uruguay in the qualifying games for the World Cup, which has given us a lot more confidence.
"I can say that we are understanding each other a lot more. But it's important to continue keeping the focus. For the moment you can say that Brazil are almost 100 per cent in the way we are playing, but of course, every game we want to improve and get the right results."
His midfield partner Kaka was equally impressed with the win, but had words of sympathy for several of his former team-mates at AC Milan, who he recently left for Real Madrid. He said: "We played very, very well today and are very happy for that. We are also happy for eliminating Italy, because it is a great national team with good players.
"It was the first time I played against Italy and for me it was important to win and we won, so I'm very happy with that. I'm sorry for my ex-team-mates Andrea Pirlo, (Gennaro) Gattuso and (Gianluca) Zambrotta, but the Brazilian team won and I am grateful for that."
Defeat for the Italians, coupled with USA beating Egypt, left all three sides on three points in Group B, well behind Brazil on nine. Egypt's goal difference was minus three, ruling them out, while the Azzurri and Americans finished on minus two but the United States went through by virtue of scoring one more goal.
Italy striker Giuseppe Rossi was disappointed with the loss, but confident that they would bounce back even stronger. "Today was a tough game," he said. "We lost 3-0 and it's sad of course because we wanted to go through. But this loss was against a very good team like Brazil.
"We had or chances and could have done better but that's football. We have great players in this team, which hopefully will be back here in South Africa at the World Cup next year. It was a tough game today, but as I said, we just have to take it on the chin and come back again stronger."
Winners Brazil will now go on to face Group A runners-up and hosts South Africa in the second semi-final on Thursday, while European champions Spain will take on USA on Wednesday.