A statement on the Newcastle website said the club were "embarrassed and appalled" by the violence that followed the 3-0 home defeat.
"Newcastle United have been working with Northumbria Police, and will continue to do so, in order to identify all of the individuals concerned," the statement added.
"The Club will take the strongest possible action against those involved in the disturbances and will impose immediate lifetime bans on all those found guilty.
"These deplorable individuals have no place at Newcastle United and bring shame on the Club and the vast majority of its proper, law-abiding fans."
Four police officers were injured when trouble broke out, with bottles thrown and rubbish bins set on fire as mounted officers tried to move crowds back to allow visiting fans to be escorted to stations.
Northumbria Police said 29 arrests were made during the game which ended in Sunderland's biggest top flight win at Newcastle since 1966 and their first there in nearly 13 years.
A police spokesman said officers were studying CCTV footage of the city centre to identify the troublemakers.
British newspapers condemned the violence in both Newcastle and at Wembley Stadium on Saturday when Millwall fans fought with each other and the police during their team's FA Cup semi-final against Wigan Athletic.
The Daily Telegraph headline ran "English Disease Returns" and the Daily Mail feared a "Return to the Dark Ages".
The violence at Wembley started before halftime but escalated during the second half and observers said many fans were either drunk or taking drugs before the fighting began.
Fourteen people were arrested at Wembley on Saturday, 12 of them Millwall fans, for offences including affray, possession of an offensive weapon, possession of Class A drugs, ticket touting and assaults on police.
Millwall have also threatened life bans against any fans convicted for their actions on Saturday.
