Costa Rica almost opened the scoring with just two minutes played, but Joel Campbell's instinctive effort from the edge of the box floated narrowly wide of the post.
England were up the other end soon after as Daniel Sturridge fired just wide before the striker shot off target again with a speculative drive from distance.
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Both teams continued to battle for possession during a hard-fought opening 45 minutes, and Costa Rica were inches away from taking the lead midway through the half when Celso Borges's free kick was tipped over by Ben Foster.
England, who looked far from a team with nothing to play for, were appealing for a penalty with around 30 minutes on the clock as Sturridge was dragged down in the box, but the referee waved away their vociferous appeals.