An estimated 200 Chilean soccer burst into the media centre about an hour before kickoff raising major concerns for world soccer's governing body FIFA and tournament organisers.
Chile wants to prevent the fans from travelling to matches abroad and ban them from stadiums at home.
"We are now studying ways of punishing these people so they will have to watch (World Cup) games from Chile from now on," FA president Sergio Jadue told reporters on Thursday.
"That also goes for local matches in Chile as well as matches with visiting national teams. We never want to see these images again," he said at the team's training ground in Belo Horizonte.
The fans, looking for a way into the stadium, charged through a security checkpoint before smashing down a glass door and invading the journalists' working area before their team's 2-0 Group B win that saw holders Spain crash out of the tournament.
Ralf Mutschke, FIFA's director of security, told reporters on Thursday 87 Chilean fans were arrested and had to leave the country within 72 hours or be deported. He described the security breach as "embarrassing".
Jadue said the Chilean embassy in Brazil was dealing with the issue and he said the FA could potentially also face a FIFA probe.
At least one Chilean fan, a woman, was injured and taken outside in a wheelchair.
There was also trouble in the Chilean capital, Santiago. As part of their celebrations, fans hijacked six buses and drove them around the city and scores of other buses were vandalised.
"We need to separate ordinary justice from sports justice. I don't know what ordinary justice in Brazil will do but our embassy is dealing with the legal issues," Jadue said.
"In terms of sports justice it could well be that FIFA will open disciplinary proceedings against Chile. Probably we need to defend ourselves. But we do not know yet what the charges could be."
Chile next play the Netherlands, with both teams having already secured their spots in the round of 16.
- Sports & Recreation