The Red Devils needed to beat Croatia to book their place in the next round, but were held to a 0-0 draw and thus finished third in their group - with Lukaku having a nightmare performance.
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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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His anger was then clear to see when he put 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."
But former Chelsea striker says blame should not all be on Lukaku.
"We cannot put the blame on someone who has been injured the last two months, he comes on for 30 minutes and you want him to win the game.
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"As a striker he should have been a bit more on his toes but it's very difficult to blame him for this."
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.
Monaco 
Stade Brestois 29 
Bordeaux 
Nimes 
Bayern Munich 
FC Augsburg 
Paris Saint Germain 
Toulouse 
CSKA Moscow 
FC Rostov 
Leicester 
Chelsea 
Valencia 
Betis 
Dynamo Kyiv 
Chornomorets Odesa 
Verona 
Inter 
Bayer Leverkusen 
FC Heidenheim 
Borussia Dortmund 
SC Freiburg 
VFL Wolfsburg 
Union Berlin 
Arsenal 
Nottingham Forest 
Everton 
Brentford 
Spartak Moscow 
Lokomotiv Moscow 
Rangers 
Dundee Utd 
Atletico Madrid 
Alaves 
Lens 
Marseille 
Ingulets Petrove 
Shakhtar Donetsk 
AC Milan 
Juventus 
ST Malo 
Manchester City 
Tottenham 
Eintracht Frankfurt 
Werder Bremen 
Girona 
Espanyol 
Feyenoord 
Heerenveen 
ST Etienne 
Montpellier 
Grenoble Foot 38 
Heart Of Midlothian 
Celtic 
Reims 
Lyon 
PSV 
Groningen