Ross Miller, 17, from Spennymoor, was arrested for his actions but he was released on bail by Northumbria Police pending further inquiries.
He (and his father Gary) visited both Newcastle's Darsley Park training headquarters and Sunderland today to apologise.
The 17-year-old told BBC Look North: "I was just overwhelmed by the fact that we had scored in the last minute against Newcastle, so I ran on to the pitch with no intention at all to push Steve Harper.
"I got a bit carried away, did what I did, which I was very sorry about, and then was taken off the pitch and taken round by the steward.
"Steve Bruce said a few words as I was led along the touchline, which he was right in doing because it was entirely my fault for pushing him (Harper).
"It was right what he said and I was wrong. He called me 'a stupid idiot', and he was right what he said because it was my fault for pushing him."
Gary Miller revealed his son had wanted to apologise to Harper in person, although the goalkeeper was not training on Monday morning and he instead spoke to club secretary Lee Charnley.
He said: "It was Ross' idea. I spoke to him at 11pm last night and it was Ross' idea.
"He wanted to do it, so this morning, off we went and we got to Newcastle's training ground and we apologised to the club secretary.
"I can't say enough about Newcastle United. As much as I am a Sunderland fan, they were absolutely great.
"He was a great gentleman, Mr Charnley. Really, we wanted to speak to Steve Harper, but we have said as much as we can. We then went to Sunderland and apologised to Sunderland.
"This isn't what we are like, this family. We have never been in trouble in our lives. It was just a one-off and we wanted to apologise, quite simply."
Sunderland AFC issued a club statement: "The vast majority of fans in the 48,000 capacity crowd behaved very well and we thank them for their loyal support.
"Sunderland AFC operates a zero-tolerance policy towards anti-social behaviour of any kind within the Stadium of Light, and we are proud of our reputation as a family club.
"Working closely with Northumbria Police, we will ensure that appropriate action is taken against anyone found to have been involved in any such behaviour at yesterday's game."
Kevin Nolan was furious at the Sunderland pitch invader who attacked Harper.
Kevin Nolan: “It’s absolutely pathetic. I’m really disappointed. They’ve scored and emotions are high, and we all know what it’s like, but that fan shouldn’t be allowed to walk into a stadium again.
“It’s not right – the safety of the players is massive. I’m not happy about it at all. Steve’s a good mate, and he said he saw him really late.
“The fella’s just pushed him over, and it’s an absolute disgrace.”
Steve Harper: “I didn’t see him until he was right on me.
“The supporter was detained by Sunderland fans after the incident, which was nice and I heard he’d been arrested.
“Niall Quinn apologised to me after the game."