Roy Hodgson's side face a tricky group with both Italy and Uruguay also expected to challenge for the two qualifying spots, and many people have already written the Three Lions' chances off.
However, Hart believes that the squad is full of "winners" and insists that they have no choice but to go into the tournament thinking that they can win it.
"Why not? We are all winners. I am going to go there with my attitude to try and win every game and if you win every game you win the World Cup. You can't go in accepting failure or defeat," Hart said in a question and answer session on Facebook.
England get their campaign underway against Italy in Manaus on June 14.