Fences have been breached by fans at both World Cup matches staged at the country's biggest and most prestigious stadium which hosts the final on July 13.
"It is embarrassing," FIFA director of security Ralf Mutschke said Thursday, one day after 88 ticketless Chile fans broke into the sold-out venue ahead of their team's 2-0 win against Spain.
Mutschke said security operations at the World Cup must "improve in order that this will not happen again."
Brazilian authorities said the fans were detained after smashing their way through a perimeter wire fence into the stadium media center.
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"We have to protect the media, there's no doubt about it -- we also have to protect the (other) fans," Mutschke said at a news briefing to address the incident.
Chile's consul general in Rio, Samuel Ossa, told reporters that the fans will be arrested if they do not leave Brazil within 72 hours and would likely have to spend time in jail while Brazilian authorities go through a process to deport them.
"They're getting off easy," Ossa said. "They were not criminals. They are people who overstepped their passion and made a mistake and have to pay for it."
But the president of Chile's football federation -- which could be disciplined by FIFA over the incident -- said the Chileans fans who invaded the stadium could face sanctions after they get home.