The midfielder, who has been convicted twice on charges of violence, blasted the BBC for giving the award to Hamilton.
The British F1 champion has been under scrutiny for alleged tax avoidance after moving to Monaco in 2012.
Barton argued that the questions about Hamilton's tax situation should exempt him from the competition, due to the BBC being funded by UK taxpayers - despite the fact that the driver won the popular vote.
The Mercedes driver told The Sunday Times' Style Magazine: "What people don't realise is that I pay tax here, but I don't earn all my money here.
"I race in 19 different countries, so I earn my money in 20 different places and I pay tax in several different places, and I pay a lot here as well."
Barton was also displeased because Hamilton took his dog to the award ceremony, and F1 is "the most boring sport ever".