Gerrard was part of the so called "golden generation" who failed to progress beyond the quarter-finals in any tournament.
This time the optimism amongst England fans appears to be more realistic particularly with the spate of injuries which have ruled out Frank Lampard, Gareth Barry, Gary Cahill and John Ruddy.
Gerrard said: "The team and squad were built up as the golden generation and the expectation and pressure grew over the years.
"We were expected to deliver in a major tournament and, by deliver, that means, going to a final or winning a trophy.
"We were put down as favourites in previous tournaments and maybe, because we haven't done that (been successful), the expectations this time will be less.
"But that could suit us and turn into a positive.
"By the same token there will be a certain amount of pressure and expectation because we are England."
Gerrard believes England can finally move past the quarter-final stage in a major competition.
He said: "It would be stupid of me to set any goals or targets. Of course, everyone's dream is to win a tournament but it would be stupid to set that as a target.
"There have been teams in the past that have won this tournament who haven't necessarily been favourites so we have to go there and do as well as we can.
"If we click and gel, if we get that bit of luck, we can get over that hurdle of the last eight."
Winger Theo Walcott believes there are encouraging signs under new coach Roy Hodgson although it will take time before England are the finished article.
He said: "We are getting used to way that Roy wants the team to set up and play.
"When you make a lot of changes, you always expect lots of little holes but I don't think that was the case. It's a positive going into the tournament.
"It's always going to take time with a new manager, the way he wants the team to play.
"It will take time but the most important thing is if we go out there in the Euros and perform well and work hard as a team, put in 100% for the fans that travel. That's all that we can ask for."
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