Jorge Luis Pinto's team thrilled with skill and ambition in shock wins over Uruguay and Italy that secured their passage to the last 16.
The pre-tournament outsiders found themselves in the unexpected position of being able to leave plenty in the tank in Belo Horizonte - an admirable achievement that did not make for an engaging spectacle.
Celso Borges had a first-half free-kick touched against the crossbar, while the bulk of England's chances fell to Daniel Sturridge - one of only two survivors from the line-up that lost the opening two matches.
The Liverpool striker found the prolific streak he displayed in the Premier League last season to have deserted him, and Roy Hodgson's team could take little from the contest aside from avoiding the ignominy of losing all three World Cup round-robin games for the first time in their history.
Uruguay's 1-0 win in a similarly scrappy encounter against Italy in Natal ensured that Group D claimed the scalps of two European teams.
Joel Campbell saw a speculative second-minute effort deflect wide and Costa Rica's control of the opening exchanges underlined the gulf in confidence between the two teams.
The 12th minute brought England's first sight of goal, Sturridge whipping a shot narrowly wide of the target following bright build-up play by Jack Wilshere.
A 15th-minute Mexican wave rippling through the Estadio Mineirao said much for the lack of intensity in a game between one side already through to the round of 16 and another with their bags packed, before Sturridge tried his luck from distance once more.
Ben Foster was the first goalkeeper called into action when he superbly tipped Borges’ free-kick behind via his crossbar.
Sturridge had a 27th-minute penalty claim rejected, going to ground under close attention from Oscar Duarte, and another half-chance fell the striker’s way, but he could not keep his header down after Phil Jones nodded Ross Barkley's corner back across goal.
Barkley fashioned space for himself in the 42nd minute, but his subsequent slice wide underscored a half desperately lacking in quality.
Costa Rica goalkeeper Keylor Navas was out quickly to thwart Sturridge as Luke Shaw’s deflected 49th-minute shot looped into his path.
Shaw was fortunate not to join Adam Lallana and Barkley in the book amid a scrappy period as the hour approached, while Giancarlo Gonzalez was deservedly cautioned for scything through the latter.
Christian Bolanos looked to do something a touch more constructive when he stung Foster's palms from 20 yards, while Sturridge exchanged passes with Wilshere and wasted his clearest opportunity of the match in the 65th minute.
A flurry of late substitutions did not increase the entertainment factor as Costa Rica looked forward to a knockout clash against the runner-up in Group C - where Ivory Coast, Greece and Japan all retain ambitions of following likely winners Colombia into the knockout stages later on Tuesday.
For England, who belatedly extended Navas when substitute Wayne Rooney sent a delicate 80th-minute chip goalwards, a grimly familiar period of reflection and attempted renewal awaits.
