Gerrard is careful not to overplay expectations but still believes England can emerge with credit from the first finals under new head coach Roy Hodgson.
He said: "Are expectations coming down all the time? Maybe with the supporters and people around looking at this squad with no Wilshere, (Tom) Cleverley, Barry, Lampard.
"Of course, people wonder whether we're capable of coping without those players. But we can't control what people say and think. We've got to get on with it and give it our best shot.
"We're quietly confident but we don't want to raise expectations unnecessarily. We're all aware that we've under-delivered in previous tournaments.
"We don't want to put too much pressure on ourselves. We want to try and enjoy the tournament and hopefully we can play at a better level."