Brazil missed a major opportunity to take an early lead when Bruno Guimaraes had his first-half penalty saved.
The breakthrough finally arrived in the 79th minute as Erling Haaland headed Norway in front. The prolific striker then sealed the victory with a superb low finish to complete his brace.
Substitute Neymar pulled one goal back from the penalty spot late on, but it proved to be only a consolation as Brazil's World Cup campaign came to an end.
"It's tough to find words in this moment," said Casemiro.
"This is a dream when you start playing football. It's a dream for any Brazilian to win the World Cup. I have a lot of pride in what I am, what all the players have done here. We had the opportunity to kill the game but we didn't.
"They then had two shots and scored. We had chances to score but couldn't convert. In the second half, we dropped our lines a bit, and we shouldn't have dropped them.
"We could have been a bit sharper with the pressing. But it's hard to say now what we should have done."
Norway will face either England in the quarter-finals on 11 July.
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