They said they would seek orders against any hooligans proven to have been involved in Friday night's incident to stop them attending future games.
So far, three people have been arrested and charged after hundreds of mainly Newcastle United fans invaded the pitch at The Northern Echo Arena, Darlington.
Chief Inspector Chris Reeves, from Darlington police, said: We will be working with Northumbria Police to identify those involved in the pitch incursion.
Pitch incursion is a criminal offence and we will be seeking football banning orders for those involved and cooperating fully with any FA inquiry.
It is not yet known what further police presence will be needed for Darlington's next home friendly against Middlesbrough on Saturday as a result of the trouble.
Both clubs said they were investigating the incident.
The FA is gathering evidence from both clubs and the referee into what happened during the pre-season friendly.
It is expected to be weeks rather than days before it announces what action it will take.
Hundreds of spectators, mainly Newcastle fans, ran onto the pitch after Sammy Ameobi scored Newcastle's second goal after half-time.
There were allegations of stewards being assaulted and supporters from both sides attacking each other.
The game restarted after a delay but some of the 9,721 crowd, more than two-thirds of whom were from Newcastle, decided to leave early.
Newcastle eventually finished 2-0 winners.
Both sides condemned the trouble after the game. Newcastle manager Alan Pardew said he was bitterly disappointed by the events, which he said would damage the club's reputation. He backed managing director Derek Llambias' call that the club would take the strongest possible action against those responsible.
Darlington managing director Graham Fordy said the Quakers would deal with any of its fans who were guilty, but added that it was a great night for the club from a sporting point of view.
When asked what changes would be made for friendlies against Middlesbrough and Sunderland, Mr Fordy said on BBC Tees last night: No rethink.
Not at all.
We just want to move on and hope there will be as many Middlesbrough and Sunderland fans as there were Newcastle fans.