The violence, which saw 11 police officers injured, had been in the planning for several weeks by gangs of Polish thugs mainly based in Dublin and Scotland.
Police have stressed that members of the Polish community living in Northern Ireland had not been involved in the violence.
Around 800 Polish nationals travelled to Northern Ireland without tickets for the game. It is understood that around 50 were involved in the organisation of the violence which flared before and after the match.
“We believe there was a hard core of Polish nationals who came to the game without tickets but with a very clear intent to cause trouble and disruption to genuine supporters and local residents,” PSNI Superintendent Chris Noble said.
“We believe these troublemakers are not local, they had travelled to Northern Ireland with the express purpose of causing trouble. Unfortunately their actions may well have put the safety of law-abiding and local Polish residents in jeopardy.
"I would appeal to all right minded people to assist these neighbours and unite with them to condemn this type of behaviour and isolate the perpetrators of this type of criminality.”
A security source told the Belfast Telegraph that those behind the violence regularly organise clashes at football matches.
“This was well organised and they will have been planning this for several weeks. Those behind the organisation of this travelled mostly from Dublin and Scotland. This type of violence is now commonplace in Polish football,” the source said.
The PSNI would not say if officers had been expecting trouble as it was “a matter of intelligence”.
Sports Minister Gregory Campbell said that the confrontation began after some Polish supporters unfurled a republican flag.
“There were some Polish fans who introduced one of the Irish republican flags, that are supportive of the group that killed the soldiers and the policeman a few weeks ago, which obviously then led to even more tension,” he added.