The Red Devils needed to beat Croatia to book their place in the knockout stage, but were held to a 0-0 draw and thus finished third in their group.
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Lukaku came on at the break, but squandered Belgium's best chances of the match that could have kept them in the tournament.
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A superb De Bruyne pass set up Carrasco and when his effort was blocked, the striker fired the rebound against a post.
There was more despair when he headed over from in front of an open goal, although replays showed De Bruyne had failed to keep the ball in.
Lukaku had another clear chance to send Belgium through in the last minute, but his bundled effort from Thorgan Hazard's cross was saved on the line by Livakovic.
The Chelsea forward was denied again by Croatia defender Josko Gvardiol's brilliant last-ditch tackle in the closing moments.
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The Inter Milan striker, on loan from Chelsea, looked like he was in tears after the final whistle and was consoled by coach Thierry Henry.
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He was then seen putting his fist through the dugout as he walked off the pitch.
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talkSPORT's co-commentator for the match, Tony Cascarino, said: "You can't get better chances than that. Romelu Lukaku has had injuries this year, he's clearly not been fit enough and could have reacted slightly quicker.
"They don't get better than tonight. Sometimes football can be very cruel and it was tonight for Belgium."
It has been a wholly disappointing World Cup for the so-called Belgium 'Golden Generation', who reached the semi-finals of the tournament in 2018.
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