The win puts Costa Rica into the last 16 from Group D and means Roy Hodgson's side will soon be leaving Brazil for home, exiting in the group stage for the first time in 56 years.
England travel to play Costa Rica in Belo Horizonte on Tuesday with nothing more at stake.
After 2-1 defeats to both Italy and Uruguay, England had been hoping for an Italy win to give themselves a glimmer of hope.
An Italy win over both Costa Rica and Uruguay - plus an England victory over Costa Rica - would have been needed.
But that ended with a header by Bryan Ruiz in off the underside of the bar for Costa Rica in the 44th minute.
"What have the Romans ever done for us?" joked former England international Gary Lineker on Twitter.
It is the first England have been eliminated at the group stage of the World Cup since 1958. The other group-stage exit came in 1950 - the previous time the tournament was held in Brazil.
Hodgson has meanwhile received the backing of Football Association chairman Greg Dyke who says there is no "great value" in changing the manager.
"We were not humiliated or anything like that, they were narrow defeats but it's for the football people not for me to identify why we didn't win," he said before the Costa Rica victory.
"He came to do a four year cycle leading up to the Europeans and we want him to stay and continue with that.
"It's disappointing to lose both games narrowly to both sides but there are some positives, there are a lot of young players who got blooded here who got into tournament football here."
Hodgson, 66, whose contract runs until the end of Euro 2016, said after Thursday's defeat to Uruguay that he did not feel the need to resign.
"I'm bitterly disappointed, of course, but I don't feel I need to resign, no, " he said.
"On the other hand, and if the FA think I'm not the right man to do the job, that will be their decision, and not mine.
"I've been really happy with the way the players have responded to the work we've tried to do."