Barton gave QPR an early lead at Loftus Road before getting involved in a tussle with Bradley Johnson and appearing to headbutt the Norwich midfielder.
QPR appealed against the dismissal but the Football Association confirmed on Wednesday afternoon that appeal had failed.
An FA statement read: "An Independent Regulatory Commission has today [Wednesday 4 January] dismissed a claim of wrongful dismissal from Queens Park Rangers midfielder Joey Barton following his red card for violent conduct in the QPR v Norwich City game on 2 January 2012.
"Barton will serve a three-match suspension with immediate effect."
It means the 29-year-old midfielder will miss Saturday's FA Cup tie at MK Dons, the Premier League clash away to former club Newcastle the following Sunday and the home match against fellow strugglers Wigan on January 21.
Barton initially used his Twitter account to claim the match officials had been "conned" and responded to Wednesday's punishment with more tweets, hitting out at the FA's ruling while also admitting he was "devastated" not to be able to face former club Newcastle.
He tweeted: "Devastated to miss return to SJP and FA cup tie but life goes on. Feel sympathy for those who have never played yet set the rules.......
"I'd be really interested to see who this "expert panel" really consists of? Wonder if we can find out?
"Right, enough on this matter, I am going to use my 3 games to take up acting classes. It's abundantly clear the best thespian wins. #nojustice."