The Selecao compounded the disappointment that had gripped the country following their 7-1 thrashing by Germany by losing 3-0 to Netherlands in Saturday's third place playoff.
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"It wasn't the end we expected but that's life and football," the 26-year-old told Bandeirante.
"Now we have to be men enough, learn from the critics that we will suffer, fair or unfair - that's part of it. I believe that, for our part, we never ceased giving our all at all times.
"We just have to thank the Brazilian people, even those who criticised us."
The Wolfsburg midfielder insisted that the Selecao could still take positives from the World Cup, most notably the way it has been hosted, and urged players and supporters alike to look to the future.
"Brazil showed everyone that it is capable of hosting a marvellous event like this World Cup without bigger problems," Gustavo added.
"We have to take good things from this. A year and a half after a title [the 2013 Confederations Cup] we reached the last four among the biggest teams in the world. So there are positives that go in our favour.
"It's time to keep working, that's the only solution. I think there are things to learn from this. Football is evolving, we watched the other teams. That's something.
"We have to live with this, we are aware of the pain and now that we'll be stained by this. But we have to move on, and look for things to get motivation from and keep moving ahead."