The Magpies midfielder has said sorry to Blackburn's Morten Gamst Pedersen for the punch that will earn him a three-match ban.
The 28-year-old had earlier been charged by the Football Association over an incident during Wednesday night's 2-1 Premier League home defeat by Rovers.
Barton said: "I fully accept that I was in the wrong on this occasion and accept the charge that the FA have brought against me.
"I would like to apologise to Chris Hughton, my team-mates, our supporters and of course to Morten Gamst Pedersen and Blackburn Rovers.
"This season, I have really been enjoying my football and although I have been on the receiving end of a few robust challenges, I have, up until now, remained calm in the face of provocation and just carried on with the game.
"But I hold my hands up, I reacted badly to the situation on Wednesday night and I deeply regret it.
"I have been working very hard to keep that side of my game under control and I think it has showed in the way I have been able to get on and enjoy my football this season.
"I look forward to trying to get back into the team once my suspension is over and helping the club maintain its good start to the season."
Barton will miss Saturday's Premier League clash with Fulham and the following two games against Bolton and Chelsea.
That will come as a blow to Hughton, who has seen the former Manchester City midfielder establish himself as a key member of the side which currently sits in fifth place in the table despite the Blackburn defeat.
Hughton said: "We accept the action taken by the FA, and it is of course disappointing to lose Joey for three games.
"He has worked so hard on his game this season, but he knows that he can't react the way he did on Wednesday."
Barton was charged after match referee Mike Jones viewed video footage of the incident, which he did not see at the time.
It happened 50 minutes into the game while the official was cautioning Rovers' midfielder David Hoilett for diving.
Barton walked towards Pedersen, who had opened the scoring in the third minute and caught him with a punch to the ribs.
The Norwegian was treated at length on the pitch and later had a frank exchange of views with his attacker, who seemed to be suggesting it had been little more than a playful slap.
Barton's career has been littered with problems on and off the pitch, although having sought professional help, he has managed to avoid trouble and rediscover something like his best form this season.
His new-found tolerance was put to the test at Wolves earlier in the campaign when, in Hughton's words, he was "kicked from pillar to post", but did not react.
However, his frustration got the better of him last night and he must now face the consequences.
Hughton, who had earlier suggested the incident had only been given such prominence because of Barton's involvement, now faces the task of finding a replacement as the Magpies attempt to bounce back against Fulham at the weekend.