Paris: Belgium coach Marc Wilmots and Republic of Ireland counterpart Martin O`Neill expressed horror Sunday at the hooligan "scourge" that has cast a shadow over Euro 2016.
Pitched battles between Russian and England fans before their countries` 1-1 draw on in Marseille Saturday has seen both teams warned about the future conduct of their fans.
The violence was the worst seen at an international tournament since the 1998 World Cup.
More than 30 people were injured and three people remained in a serious state, including an Englishman who was beaten around the head with a metal bar.
Wilmots said everything must be done to ensure fans can attend future European Championship matches without fear of any repeat of the violence.
"I have seen something horrible (in the coverage from Marseille), which was a father, with his son, running away in the stadium," said the Belgium boss after Russian fans attacked English supporters at the Stade Velodrome following the match.
"We need to rid football of this scourge, but how we do that, I don`t have the answer.
"People generally enjoy themselves when they go to grounds and we need to make sure that continues."
European governing body UEFA has threatened to throw both countries out of the tournament if there is any further trouble, but Wilmots says that may not solve the problem.
"I think it`s a very difficult debate, it has nothing to do with what happens on the pitch," he added, with Belgium to face Italy on Monday in their opening game in Lyon.
"We have penalised players in the past, because of the actions of so-called fans."
O`Neill echoed the concerns, lamenting the return of extreme violence that plagued football in the past but highlighting the difficulty of stamping it out.
"The scenes down in Marseille are pretty tragic, something we thought we might not see for quite some considerable time," said O`Neill, ahead of Ireland`s opening match against Sweden in Paris on Monday.
"To start off on that note is quite unedifying, it`s pretty shocking.
"UEFA have come out and condemned it in pretty strong language and I think everybody feels the same. It`s a poor start for the competition. I hope it can be sorted out.
"People say segregation wasn`t strong enough but I think if people are setting out for trouble they`ll cause it regardless."