England will head to Poland and Ukraine next week without long-term absentee Jack Wilshere and recent casualties Gareth Barry and Frank Lampard.
Gerrard is careful not to overplay expectations but still believes England can emerge with credit from the first finals under new manager 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, 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."
Faith in Henderson
Gerrard has faith in his Liverpool team-mate and fellow midfielder Jordan Henderson, who has been called into the squad after Lampard was ruled out with a thigh injury.
He said: "Jordan has had a little bit of criticism but, credit to him, he's played through it. He was getting stronger and stronger towards the end of the season.
"He did well when he came on against Norway. The manager's seen a lot of him in the U-21s where he's been fantastic. He's got a very bright future. People judge Jordan on his price tag, rather than his age, his potential and what he's going to do in the future.
"He's still got everything ahead of him. I was nowhere near the finished article at 20-21, and had a lot of learning and improving to do, and I'm sure Jordan will do the same.
"He's a very good passer, very fit, looks after himself, doesn't touch alcohol, has got a body a lot of footballers would be jealous of. He's a big strong lad who can get about the pitch."
Gerrard believes Hodgson is already building up a solid understanding with the England squad despite only having been together for the past ten days.
"Sometimes with managers, it takes time for messages to get across, but I can already see signs that the players are adapting to Roy's style," he said.
"Even yesterday in training, he split the defence and the attack up and he's drilling in his methods and his ideas. He gets his message across very clearly. I'm sure the players will take it on very quickly."