Hodgsons side have been placed alongside Italy, Uruguay and Costa Rica in Group Din 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.
Theres 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 well come away from the World Cup knowing that if wed just been a bit more relaxed and our minds were a bit more free we couldve done a bit better.
The fear is that the pressure gets on top of the players and we arent 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.