Few had Costa Rica pegged to accomplish much in the "group of champions", but Los Ticos proved their mettle earlier in the tournament with wins over Uruguay and Italy in their first two group-stage matches.
Both sides created ample scoring chances over the course of Tuesday's 90 minutes, but the finishing was just a tad off as Costa Rica claimed the point it needed to win Group D.
Los Ticos will face the runner-up from Group C on Sunday, while England finished its group campaign with just one point and secured its worst-ever World Cup placing.
Despite going out of the tournament after just two matches, Roy Hodgson's side was hoping to save some face with a win in their final match in Brazil, and the Three Lions had the better of the play early on.
Liverpool man Daniel Sturridge had the first clear-cut opportunity with a strike from the top of the penalty area in the 12th minute, but the strike flew wide of the Keylor Navas' right post.
Sturridge created most of the scoring chances for England in the first half and had a second chance in the 18th and a third in the 27th as a cross fell to his feet in front of goal, but Navas was out quickly to collect the ball.
Ten minutes before the break it was Sturridge again with a chance off a corner kick, but his header sailed over the crossbar.
In the second half, Los Ticos created a fair amount of chances to break the deadlock, with the best opportunity coming in the 63rd minute as Cristian Bolanos ripped a strike on goal from distance but it was parried away by England goalkeeper Ben Foster.
England pushed forward for most of the second 45 minutes looking for a winner as just a few moments after Bolanos' attempt, Sturridge and Jack Wilshere worked a nice one-two to send Sturridge through on goal, but the strike with his favored left foot was inches wide of the far post.
The fourth official's board showed only a couple minutes of stoppage time and the Three Lions were unable to fashion a winner to bow out of the World Cup without a win and just one point.