Ralf Mutschke says changes will be made after a large crowd supporters stormed the stadium's press center prior to Wednesday's match in Rio de Janeiro.
A large number of supporters broke through an outer gate before forcing open the door to the press center entrance and tearing down part of a temporary partition wall in a bid to gain access to the stands prior to Chile's sensational 2-0 victory over world champion Spain on Wednesday.
They were then pinned down by stewards in a corridor next to the media center and held there until Rio de Janeiro's federal police arrived to take them away.
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On Thursday, FIFA confirmed that 87 people were detained by state authorities and have been given 72 hours to leave Brazil in accordance with state law.
But questions remain as to how such a large group of ticketless fans managed to evade a series of police ticket checks to reach the vicinity of the stadium, particularly after around 30 ticketless Argentina supporters scaled an outer wall and broke through a gate prior to their team's clash with Bosnia-Herzegovina at the Maracana on Sunday.
"It is embarrassing," FIFA's director of security Ralf Mutschke told reporters. "We have to protect the media and there’s no doubt about it. We also have to protect the fans. We had meetings last night and this morning to assess the situation and I'm confident that with the measures being discussed, this will not be repeated."
Hilario Medeiros, security general manager of the Brazil 2014 local organizing committee, praised the work of the 1037 private security personnel employed at the stadium Wednesday for handling the match according to procedures and revealed no injuries had been reported as a result of the incident.
"The stewards did their job without provoking panic or violence," he said. "Problems are happening but the contingency plans are all in operation. We had no fans enter the stadium without being detained. We have to consider all the facts [of the incident] and react, and we will react to ensure the stadium integrity is guaranteed."