The 28-year-old was charged by the Football Association on Thursday for punching Rovers' Norway midfielder Morten Gamst Pedersen in the chest, which was not seen by the referee.
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"I fully accept that I was in the wrong on this occasion and accept the charge that the FA have brought against me," Barton said in a club statement before apologising to all involved.
"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."
Barton was given until Friday to reply to the charge and under the FA's fast-track regulations his admission means he will now be handed a standard three-match ban.
Newcastle manager Chris Hughton said: "He has worked so hard on his game this season, but he knows that he can't react the way he did on Wednesday."
