England had chances to rescue something form a terrible campaign but Daniel Sturridge sent both shots wide.
Costa Rica, who only made the last 16 on one other occasion in 1990, defied the tag of minnows and outsiders in the group to beat both Uruguay and Italy. Uruguay seized second spot with a 1-0 win against 10-man Italy in Natal.
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Costa Rica did test England goalkeeper Ben Foster on one occasion as Celso Borges' long distance freekick forced him to leap to tip the ball over the bar.
England pressed hard from the start with Costa Rica's impressive goalkeeper Keylor Navas getting down bravely to thwart Sturridge and then saving well from Southampton winger Adam Lallana.
Sturridge should have given England the lead in the 65th minute as Jack Wilshere's beautifully weighted pass into the area saw the Liverpool striker run on to it but he sent the ball past the far post.
England coach Roy Hodgson sent on veterans Steven Gerrard -- probably for his last appearance in an England shirt -- and Wayne Rooney in a bid to grab a late win but it was all in vain as the Costa Ricans held them at bay.
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