Pardew claimed the fans, who were responsible for causing a 10-minute delay in the match as celebrations of Sammy Ameobi's 55th-minute goal turned ugly, had brought shame on theclub.
Ugly scenes: Fans confront Newcastle's Joey Barton during pitch invasion
The match, which United won 2-0, looked in danger of being called off as scenes turned violent at The Darlington Arena and, although calm was eventually restored, the guilty parties can expect repercussions.
Three fans were arrested and another escorted from the ground.
Pardew said: 'Having reflected overnight on yesterday's match at Darlington that was interrupted in thesecond half by the actions of some of our supporters, I am left bitterly disappointed by the events that unfolded after Sammy Ameobi scored our second goal.
'Apart from the frustrating disruption to what was a very good game of football and an important part of our pre-season preparation, the pitch invasion was totally unacceptable and has brought shame on everyone connected with Newcastle United.
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'We came to play a football match and to provide entertainment for a family audience - instead we witnessed some truly appalling behaviour which damages the reputation ofthis great club and the vast majority of our true and law-abiding supporters.
'As (managing director) Derek Llambias said yesterday evening, the club will now be taking the strongest possible action against those individuals responsible and thatcan't happen soon enough. I speak for everyone at Newcastle United whenI say I never wish to see those scenes at a football match again.'
Llambias was quick to condemn the actions of the supporters last night, insisting the Magpies would do allthey could to identify those involved.
He said: 'The club will be seeking to obtain footage of the disorder from Darlington FC and the police and will be taking the strongest possible action against those individuals responsible for the shameful behaviour.
'This behaviour is not typical of the vast majority of our fans, however this incident gives a poor impression of Newcastle United and its loyal supporters.'
Watch video of the pitch invasion
Durham Police confirmed three visiting Newcastle fans were arrested for 'pitch incursion' and another was escorted from the ground.
Pardew reportedly intervened to try to calm fans down and appeal for them to clear the pitch.
Some of the 9,000-plus crowd thought the match had been abandoned but the referee managed to restart the game after the playing surface was cleared.
Police could not confirm reports of an isolated outbreak of fighting between fans during the match.
After the game Pardew blamed the disorder on young fans losing their heads.
He said on BBC Radio 5 Live: 'I think a few younger members of our fan group just lost their heads a little bit over something, I don't know. It was difficult to assess fromwhere I was standing - I was on the other side of the pitch.
'I just thought 'we want to get theplayers off'. Usually that gets the fans off if there's nothing to react to. I went over there myself to try to plead with them to stay off.'
Durham Police said they have charged three people following the pitch invasion.
A 22-year-old man, a 21-year-old and a 17-year-old were detained.
Durham Police said the 21-year-old, who is from Newcastle, was charged today with going onto a play area and disorder. The 22-year-old, who is from Gateshead, was charged with going onto a play area and a public order offence.
Both men will appear before Darlington Magistrates Court on July 26.
The 17-year-old youth was charged with going onto a play area and will appear at Darlington Youth Court on August 5.
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