The Football Association will push for life bans to be imposed on the fans whose behaviour marred last night's Carling Cup tie between West Ham and Millwall.
The FA are looking into the events that saw a man stabbed outside Upton Park and pitch invasions occur following the Hammers' goals.
West Ham have pledged to help with the investigation into the shocking scenes but could also face action themselves.
A spokeswoman for the Metropolitan Police said officers had made several arrests and were scanning CCTV footage to identify hooligans.
FA director of communications Adrian Bevington said on BBC Radio Five Live: "We have to understand exactly what measures were put in place last night.
"I'm not going to condemn West Ham or Millwall football clubs for any of their actions - certainly not at this stage, because we don't know exactly what's been put in place.
"And we know there have been huge efforts on the parts of all our clubs to try to eradicate the problems and we've had a history of success on that.
"However, we have to make sure that the individuals concerned face such tough actions that they can't go to football again.
"We all want a big atmosphere at matches - that's part of football, part of the passion.
"However, we also want to make sure it's a safe environment to watch games and we've just spent the best part of 20 years working towards that."
Football Supporters Federation chairman Malcolm Clarke, due to meet with FA chief executive Ian Watmore today, recognised the "very serious" nature of the crowd disturbances but stressed that "hysterical over-reactions" to the incidents would not be helpful.
"It's not a good start to the season and it's important a full investigation is done, and the FA are going to do this with all parties to see exactly what caused this," Clarke said.
"But I think at this stage we must keep it in perspective.
"Certainly over the last 20 years the amount of football violence has radically reduced.
"It's too early I think to start drawing too many long-term conclusions, but obviously this was a very serious incident."
Clarke added: "I can assure you the vast majority of Millwall and West Ham supporters will be as horrified by events that occurred as everybody else.
"It's important to get to the bottom of it but too many hysterical over-reactions don't help."
Clarke explained: "I have a routine meeting with the FA chief executive today - I'm quite sure this will now be on the agenda.
"There clearly needs to be a very clear response to try to make sure this doesn't happen again."
However Clarke is aware that football still has a hooliganism problem, even if such large-scale incidents are are.
"We haven't eliminated it, that's certainly true," he said.
"We haven't yet had figures for last season but Home Office figures for the four previous seasons to that showed the lowest level of disorder since those records started being kept."
He added: "Anybody who goes regularly to football matches and has done for 20 or 30 years as I have, is in no doubt that the amount of disorder is far less than it was, say, 20 years ago.
"That is not to diminish last night, that was obviously an extremely serious matter.
"The question is, why did it occur at that particular game when the trend over recent years has been in the opposite direction?"
Given West Ham and Millwall are two leagues apart, a repeat of the Upton Park clashes is unlikely to occur in the near future.
Clarke urged those who look at last night's disturbances to examine whether the authorities were prepared for all possibilities.
"Part of the investigation would need to look at whether appropriate measures were put into place to deal with the situation," he said.Reuse content