Coach Luiz Felipe Scolari heaped praise on Chile after his Brazil side moved into the World Cup quarter-finals thanks to a 3-2 penalty shootout victory over their South American rivals.
With the scores level at 1-1 after extra-time, Neymar's penalty in the shootout proved decisive when Chile defender Gonzalo Jara smashed the final spot-kick against the post.
Julio Cesar saved two penalties in the shootout as the hosts booked a last-eight encounter with Colombia, who were 2-0 winners over Uruguay.
Brazil were pushed to the very end by Chile, who could have won the absorbing contest in Belo Horizonte had Mauricio Pinilla's shot in the last minute of extra time gone in rather than hit the crossbar.
Scolari paid tribute to Jorge Sampaoli's side and insisted his own team showed tremendous spirit to remain in the competition.
He told FIFA.com: "We knew when the draw was made we were going to be in for a tough time.
"They're a very organised team with a good tactical system and fine players.
"Every credit to Chile but this penalty shootout win says a lot about us and about our desire to progress.
"The players can have a break now and, as they recover, we'll have a look at how we won, go through all the tricky situations we were in and a whole lot of other details.
"The idea is to build on this. When you win like this you come out stronger. We're going to tell them that so they can appreciate what they've done."
Brazil had taken the lead through a goal awarded to David Luiz - even though it appeared to come off a Chile player - before Chile netted a deserved equaliser through Alexis Sanchez.
Brazil's win also saved English referee Howard Webb from becoming the country's public enemy number one after he found himself at the centre of huge controversy when he disallowed a goal by Brazil forward Hulk for handball.
Sampaoli believes his side were unlucky to bow out of the tournament and can be proud of their efforts.
He said: "I'm not happy. We gave everything we had and we were up against a whole stadium, against the hosts and we didn't go through.
"Our players made history and they did their country proud. We had possession of the ball, we put in a lot of effort, we took more risks and we fought till the end.
"If that (Pinilla) shot hadn't hit the bar, then everything might have been different. But it wasn't. I hope that the pain that we're feeling right now becomes something else in the future.
"With time we'll look at it differently and we'll come to appreciate what this team has done."
"There's huge pressure in representing our country, and it was tough on a psychological and emotional level." - Julio Cesar
Man of the match Cesar insisted Brazil's victory went a long way to erasing the hurt caused by their World Cup exit at the hands of Holland in South Africa four years ago.
He said: "We had a good first half and created a lot of chances. After the equaliser Chile came into the game and made life hard for us.
"All we can do is thank the fans and our team-mates for keeping the faith.
"There's huge pressure in representing our country, and it was tough on a psychological and emotional level.
"I got very emotional four years ago, and today I was crying again, but this time out of happiness.
"Not many people know what I've been through, but I knew my international career wasn't over.
"We've got three more steps to go now and I want to see Brazil celebrating. That's my big dream."