Gerrard, who recently retired from international football, cite the example of both Wayne Rooney, who succeeded him as captain and will make his 100th appearance in Saturday's Euro 2016 qualifier, and Liverpool team-mate Raheem Sterling as cases in point.
Both Rooney and Sterling made their England debuts aged 17, with Rooney often since being portrayed as the saviour of a national side that has not won a major tournament since lifting the World Cup on home soil back in 1966.
"It is his own fault for being so good," said Gerrard of Rooney in an interview with ITV Sport.
"It is almost a compliment to Wayne because he is so good and the press know on his day he is a world-class player who can create magical moments," the 114-cap midfielder added.
"It is only normal he is getting all the attention. Wayne has had it for years but he has handled it well.
"But I think maybe our country is guilty of putting too much pressure and spotlight on any one individual.
"You start to see similar things now with Raheem Sterling.
"It has always been the way; the media and punters try to grasp onto that one hero and hope he is going to be the person who makes everyone happy at a major tournament."
Sterling found himself in an uncomfortable spotlight during the last international break when England manager Roy Hodgson sparked a debate about his fitness after saying the Reds star told him he was feeling tired ahead of the qualifier in Estonia.
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