The Three Lions secured their place in Brazil on Tuesday night thanks to a 2-0 win over Poland in their final qualifier.
However, Barnes believes that Roy Hodgson's side will need plenty of luck if they are to lift the trophy.
"England can win it if everyone else underachieves and we play to our maximum," he told BBC Sport. "But the chances of that are not very high."
The draw for the group stage of the 2014 World Cup will be held on December 6.