Fagner called on Brazil to learn from Tuesday's defeat to Peru, although both he and Marquinhos criticised the LA Memorial Coliseum pitch.
Brazil were beaten for the first time since their 2018 World Cup reverse to Belgium, ending a 17-match unbeaten run, as they lost 1-0 to a late Luis Abram goal.
But Fagner insists the South American champions never questioned the threat of their opponents, who they defeated in the Copa America final.
The right-back, who started, with Dani Alves on the bench, hoped Brazil would be able to grow from a rare loss.
"We know the strength of South American football. There is no poor team," Fagner told TV Globo. "We played a consistent game and created chances to score. We were penalised by a set-piece at the end of the game.
"We need to grow and mature as soon as possible with these types of games to improve for the World Cup qualifiers.
"These games have to make us grow as a team. We know the importance of winning, of working calmly towards victory. But we also know that defeats can happen. This has to make us grow."
Fagner added the firm pitch in Los Angeles, used to hosting American football games, "undoubtedly" contributed to the defeat, and team-mate Marquinhos concurred.
"I think it was a very close game. We came from two good games against them and good results," Marquinhos said. "We knew they would come for the result and they did what they had to do.
"The pitch didn't help much. The ball bounced a lot. We tried to force passes through the middle, but both teams misplaced a lot. We knew it was a one-goal game and they were happy from set-pieces."