
But a late strike from substitute Mladen Petric restored Croatia's lead and England could not find the third equaliser they needed.
Russia's win in Andorra meant they qualified alongside group A winners Croatia.
England coach McClaren made a couple of brave decisions before the match, leaving out David Beckham in favour of Shaun Wright-Phillips and handing Scott Carson the goalkeeping gloves in place of Paul Robinson.
In sodden conditions with teeming rain, England played a 4-5-1 formation but their plans were in tatters within 15 minutes as Croatia took a 2-0 lead.
A horrible mistake from Carson handed Slaven Bilic's team the lead as Nico Kranjcar's long-range shot squirmed through his grasp after just eight minutes.
Six minutes later, things got even worse for England as Edouardo, of Arsenal, played a superb through-ball to Ivica Olic and he rounded Carson to double his side's lead.
England looked listless but they came out firing on all cylinders after the break, with Beckham and Jermain Defoe brought on for Gareth Barry and Wright-Phillips.
The decisions lifted the England side and McClaren's side got back in it when Frank Lampard scored from the penalty spot after a spot of shirt-pulling on Defoe from a Croatia defender.
Carson then made a brilliant point-blank save to keep England in it and the home side's hopes were were very much alive when a brilliant cross from Beckham found Crouch and the Liverpool man took the ball down on his chest and then slammed in the equaliser.
But just as England thought they might have done enough, Croatia broke away on the counter-attack and a superb first-time shot from Petric proved found the corner, though Carson got his fingers to it.
Darren Bent fired a snapshot just over the bar with five minutes to go but that was really their last chance and Croatia hung on to win the group and knock England out.
Deutsche Presse-Agentur
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