Jurgen Klopp's men lost 1-0 away at holders Real Madrid, who went into the last-16 second leg tie with a 5-2 aggregate lead.
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And it was Karim Benzema who yet again dealt the crushing blow, with the Frenchman adding to his two goals at Anfield in the first leg.
The ex-Lyon striker also scored in the Champions League final between the two teams in 2018.
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Few would have expected the Reds to overturn the three-goal margin, with even Klopp conceding that it was highly unlikely his side would advance into the quarter-finals.
But the Merseyside outfit certainly had their chances, and were unlucky not to have scored in the first half at the Bernbaeu.
Darwin Nunez should have broken the deadlock early on after he was played through by Mohamed Salah but his tame shot when one-on-one with Thibaut Courtois was easily saved as he rolled it harmlessly down the middle of the goal.
Diogo Jota then spurned the next chance for the visitors after being found by Salah, but he got his left-footed attempt all wrong.
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Nunez again tested Courtois with a looping header and a curling strike, while Cody Gakpo forced the Belgian shot-stopper into action with a fierce drive.
But it was Real that had the better chances, as Alisson expertly denied Benzema from tapping home from a few yards out, while also showing great reflexes to keep out Vinicius Jr from point-blank range.
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And he somehow managed to tip Eduardo Camavinga's strike from distance onto the bar.
Klopp would have been pleased by his side's battling display, but his team struggled to carve out any opportunities in the second half as Real began to control the game.
And they finally got their reward in the 78th minute when Benzema fired home into an empty goal after Vinicius Jr squared the ball to him inside the box.
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Liverpool pressed for a late equaliser, but there was no real quality when they got in the final third with Real never looking in danger of conceding.
After winning two trophies last season, Liverpool will finish this campaign without any major silverware having also been dumped out early in both the FA Cup and Carabao Cup.
And attention will now turn to trying to secure Champions League football next term with the club currently sitting in sixth spot in the Premier League.
Their recent defeat away at Bournemouth leaves Liverpool six points adrift of fourth-placed Tottenham, though they do have a game in hand over Spurs.
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