Many have perceived England's performances to be encouraging ahead of future tournaments, and Southgate has acknowledged that his players will now be regarded in a different light.
At a press conference, the 47-year-old told reporters: "If we want to play for England we have to deal with expectation. We have raised expectation and I don't have a problem with that because we have also raised belief in the players.
"They now see playing for England as enjoyment, fun and not feeling under siege. There is an energy and connection back."
England face Belgium in the World Cup third-place playoff on Saturday.