Barton was hit with the lengthy ban and fined £75,000 by a FA-appointed independent regulatory commission on Wednesday, after being dismissed for elbowing Carlos Tevez and then kicking out at Sergio Aguero as he left the pitch in the match on May 13.
QPR are now carrying out their own investigation into the incident, and said in a statement: "Queens Park Rangers Football Club can confirm it has now started a full internal investigation in relation to Joey Barton's dismissal and subsequent events against Manchester City on the final day of the 2012/13 Barclays Premier League season.
"The QPR midfielder will not appeal against the independent regulatory commission's decision made on Wednesday and he and his team are now working in full cooperation with the club to assist in the internal investigation.
"The club expects the investigation to last at least two weeks. During this period, no one from the club or Joey Barton himself will make any further comment."
Barton, who also attempted to headbutt Vincent Kompany after clashing with Tevez and Aguero, received an automatic four-game suspension, with the additional eight matches a consequence of the manner of his dismissal.