Hodgson's side have been placed alongside Italy, Uruguay and Costa Rica in Group D in Brazil.
England were eliminated in the first knockout round at the 2010 World Cup, and Hodgson is fearful that his players may be affected by external pressure.
"There's a lot of pressure from family and friends, those type of things," said Hodgson, who will name his initial 30-man squad on May 12.
"My biggest fear is we'll come away from the World Cup knowing that if we'd just been a bit more relaxed and our minds were a bit more free we could've done a bit better.
"The fear is that the pressure gets on top of the players and we aren't able to get close to what I know this team can produce."
England have not made it past the quarter-finals of the World Cup since 1990.
