Sunderland boss Steve Bruce apologised to Newcastle's Steve Harper after a home fan was reported to have pushed the goalkeeper at the Stadium of Light.
The supporter was understood to have got on to the pitch after Sunderland's equaliser in the 1-1 draw.
"We can only apologise - thankfully Steve is not bad," said manager Bruce.
"Well done to the Sunderland fans who gave the supporter up to the police. When I saw the age of him it looked like he was still in school."
The Football Association says it will investigate the crowd trouble and is awaiting the referee's report. "We are gathering information," said a spokesman.
Northumbria police said a 17-year-old was arrested on suspicion of entering the field of play and released on police bail pending further inquiries.
Bruce added: "I just really can't understand society today. What goes through his mind when we have just scored with a minute to go?
"Why the hell he has got to come on to the pitch and confront Steve Harper baffles me.
"When you see the age of this young kid, it is quite remarkable how he has got that in his mind, to run on to the pitch."
Newcastle boss Alan Pardew added: "If you get last-minute goals then you get an overreaction. The boy was stupid."
Newcastle switched off for equaliser - Pardew
There were ugly scenes after the final whistle too as rival fans hurled seats at each other and the Football Association will await referee Howard Webb's report.
Police said they made a total of 33 arrests arrests before, during and immediately after the match for offences including drunk and disorderly and disorderly conduct, but said the vast majority of the 48,000 crowd were well behaved.
Temporary Chief Superintendent Steve Neill said: "The crowd was mainly good natured and the overwhelming majority wanted nothing more than to enjoy the action on the pitch in an atmosphere free from violence and disorder.
"However, there were still some troublemakers who were determined to spoil things for the genuine fans."
Webb had also spotted the earlier incident involving Harper and made sure stewards and police knew who the alleged offender was.
Meanwhile, Bruce was left a relieved man as a result of Asamoah Gyan's stoppage-time goal which prevented their north-east rivals from recording a Premier League double this season.
"It's always nice to nick a point with 30 seconds or so to go," added the Black Cats manager.
"We played well for large periods in the first half but we forgot how to play after Newcastle's goal in the second half.
"We went forward far too early and quickly. It's vitally important to get the first goal in derbies and Newcastle got that. Our response today was to never give up but we could have passed the ball better."
Meanwhile, Bruce's counterpart Pardew said the draw felt like a defeat.
Equalising goal was lucky - Gyan
"We had a good attitude to the game. We controlled and passed the ball," stated the former Reading and West Ham boss.
"Towards the end we started to get tired. The referee played a lot of injury time and during that time they got a break and two points went away. It feels like a defeat.
"With what happened to them at our place [Sunderland lost 5-1 in October] I knew they would show a lot of passion, but I think we matched that.
"Our back four were strong again and Harper didn't have to do much. It would have been our third successive clean sheet in the league."
Pardew also reiterated that his star striker Andy Carroll, who is currently out injured, would not be leaving St James' Park during the January transfer window despite speculation
linking him with a £30m move to Tottenham.
"They can put together whatever they like. He is not for sale," added the Newcastle manager.
"I am going to say it one last time, he is not for sale."
Pardew said he was be hopeful Carroll would be fit for the visit of Tottenham next weekend.
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