The 66-year-old wants the Three Lions to be relaxed at the World Cup this summer but is concerned that the expectations back home will affect his players' mindsets
The Three Lions, who were eliminated in the first knockout round in 2010, have been placed alongside Italy, Uruguay and Costa Rica in Group D in Brazil.
And the 66-year-old is concerned that high expectations back home could prevent the squad from being relaxed enough to do themselves justice.
"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, to the press.
"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.