The media executive seemingly dismissed the Three Lions' prospects with a cut-throat gesture when they were drawn against Italy, Uruguay and Costa Rica in the group phase, much to Barton's disgust.
"Nobody believes we can win the World Cup so we ain't going to win it," Barton told BBC Sport. "Greg Dyke's reaction to the draw says everything I need to know.
"I would have sacked him on the spot, because if he doesn't believe we can win it what is the point in taking part?"
Barton went on to insist that England lack world-class players, and question whether Wayne Rooney has the right mentality to make an impact on the international stage.
"Our players are not world class. Wayne Rooney could have been but look at his mentality compared to Cristiano Ronaldo - they're polar opposites," he added.
"Why does Ronaldo achieve what he has achieved and Rooney doesn't? Well when you see Rooney smoking cigarettes, does he live his life correctly?
"People who have worked with both say Ronaldo was in the gym, honing his game. The level of discipline Ronaldo has for his profession is the reason he is the best player in his position and the reason Rooney isn't."
England's World Cup campaign gets underway against Italy on June 14.