Ralf Mutschke, FIFA's director of security, told reporters that 87 Chilean fans were arrested after the incident and had to leave the country within 72 hours or be deported. (Agencies)
"It is embarrassing. We have to protect the journalists and the media and we also need to protect the fans," he said.
The Chile fans broke through security cordons and rushed through the metal detection checkpoints before running into the media centre which can accommodate around 1,500 media in a vast workroom inside the stadium.
Naturally, with so many journalists around, they were photographed and recorded with the images instantly posted on social media outlets and published in newspapers.
The fans did not appear to be looking for expensive photographic equipment or laptops but smashed down a partition wall as they made their way further into the stadium to try to reach the concourse and the seating areas.
"They broke down a gate at the outer perimeter and then kicked at the door of the media centre. We have met this morning to make sure it will not happen again," Mutschke said.
One reason the security break-in is so embarrassing for FIFA is because it followed a series of complaints about staff confiscating items like bananas, water bottles and shirt-hangers from working journalists.
In a statement read at the media briefing, Gianni Merlo, the Italian chairman of AIPS, the international journalists association, said: "AIPS is aware of concerns raised previously by colleagues concerning thefts from lockers, inadequate catering exacerbated by the petty confiscation of minor items of food and drink and even of a coat hanger which, for the broadcast journalist concerned, counted as professional equipment.
"We call on FIFA to ensure that the focus of security staff within the FIFA Zone is directed at real security for the sake of all working journalists."
However, Hilario Medeiros, the security manager for the Local Organising Committee implied it was not the fault of his organisation, saying that "all protocols" had been followed.
Andrey Passos Rodrigues, FIFA's extraordinary secretary of security for major events, insisted the matter had been dealt With.
"As far as we are concerned no important incidents have taken place," he said. "There was no fan violence in the stadium."
The briefing then descended into a shouting match between Brazilian journalists and officials with one describing the security measures as a "fiasco" and saying 200 locally hired private security officials had failed to show up for work at Fortaleza.
Fireworks were smuggled into the stadium in Cuiaba at the Chile v Australia match on Friday, although Mutschke said stewards "dealt swiftly" with that situation.
Mutschke also revealed that before Wednesday's match a "table full of butterfly knives and fireworks were confiscated at the security check-in," and that security was being constantly re-evaluated on a daily basis.
Ralf Mutschke, FIFA's director of security, told reporters that 87 Chilean fans were arrested after the incident and had to leave the country within 72 hours or be deported.