"There is no truth I'll be making any announcement on my England future in the next week. I won't be rushing into any decision. It's not the right time," the 34-year-old Liverpool midfielder said, sitting alongside England manager Roy Hodgson.
"I'm hurting very badly and broken from what's gone on in the last couple of weeks. I need to get away over the summer," added a subdued Gerrard, who has 113 caps for his country.
But despite England's exit, sealed by defeats against Italy and Uruguay, Gerrard said he was confident England can still enjoy a bright future.
"The talent is there. At the moment, it is very difficult for myself, the players, to find a lot of positives," he said.
"When you look at the bigger picture, things can change very quickly in football.
"I think we have got world class players and I think we've got players with world-class potential.
"But these tournaments only come around every two years. We'll have to wait and see."
Unlike some of his predecessors Hodgson has so far been spared the kind of scathing criticism that usually accompanies England's departure from major tournaments.
He said he was grateful to the FA for their backing in his role despite the failure to reach the last 16.
"It's a fantastic job and I'm privileged to work with such a talented bunch of players," Hodgson, who is midway through his term as manager and will lead England into qualifying for the Euro 2016 tournament in France, said.
"I think we are on a good path, and I see a lot of possibilities for these players and this team to improve and get better (and) I'm very pleased to be the man to lead them.
"Scapegoats are always needed in times of failure, but one would like to think the work you do is judged over a long period of time."
"The team prepared well, the players were first class and their attitude and desire I can't fault. We are very, very disappointed for the fans but we did try our very best," Hodgson, who was also in charge at Euro 2012, said.
He said he planned to try to give all the fit players in the squad some time on the pitch in their final game in Brazil on Tuesday against group leaders Costa Rica in Belo Horizonte.
England were knocked out with a game still to play in Group D following Costa Rica's shock 1-0 win over the Italians on Friday - a result that put the central American nation through to the last 16.
It is the first time they have not made it out of the group stages since 1958 and the first time they have been eliminated after just two matches.
(Writing by Tony Goodson; editing by Martyn Herman)
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