The Three Lions qualified for the tournament by finishing top of their group and the Liverpool legend feels that the challenge now is for Roy Hodgson's men to get past the quarter-finals.
"The dream would be to come away from a tournament and everyone back home is proud of the team," Gerrard told the Daily Mail.
"To be clapped home would be amazing. But it will only happen if we go past the quarter-final.
"For me the ambition is this: can I help get the team past a quarter-final? I haven’t really thought about what I will do after the World Cup. It is all about going to enjoy this World Cup.
“What an experience it will be in Brazil. I am absolutely delighted to help the team get there, it was a great achievement. But now the attention has to switch to: what can we do there?”
The Three Lions are currently preparing for friendlies against Chile, on Friday, and Germany, on Tuesday, with Gerrard aiming to add to his collection of caps.
"One hundred and seven caps isn’t bad for someone who isn’t ‘a top, top player’, is it?" he added, referring to remarks made by Sir Alex Ferguson in his recent autobiography.
"I never expected to get that amount of caps. When I made my debut, I set myself the personal target of trying to get 50 caps and score 10 goals if I could.
"So to have 107 is something I am really proud of, particularly being among those names.
"I’m not looking at [Peter] Shilton or [David] Beckham. Passing Bobby Moore would be the next one. To go past him, after everything he did, would be unbelievable.”