Liverpool were left to rue missed chances with Real Madrid ultimately progressing to the semi-final after a goalless draw at Anfield.
Starting with a 3-1 deficit from the first leg, the task always looked difficult for the Reds but playing with a vigour reminiscent of their sides of the previous two seasons they made life hard for their opponents in the first half.
Mo Salah especially was presented with a number of chances, the best of which came in the first three minutes when he could only shoot straight at Thibaut Courtois from inside the penalty area.
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As the game went on the Spanish champions looked more comfortable and Karim Benzema, whose deflected cross hit the post in the first half, should have done better with a free header nine minutes from time.
Zinedine Zidane's side will now face Chelsea in the semi-final.
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Jurgen Klopp’s gegenpress or heavy metal football has been conspicuous by its absence this year but it returned turned up to 11 in the first half and make no mistake it rattled Real Madrid.
If Salah had scored when presented with a golden chance in the third minute things could have been very different.
He had chances to redeem himself but with his confidence down either fired over the bar or saw his effort blocked.
It will be interesting to see whether Klopp can rouse his side for similar efforts in the final league games of the season, but they will need their forwards to finish this hard work if they are to ascend the long way to the top four.
Man of the match – Trent Alexander-Arnold
He may not be a great defensive right back, but if Gareth Southgate cannot see he must be in the England squad after watching this game something is seriously wrong.
No one can pick out a pass like him in the England team. He can manipulate a ball with the inside or outside of his boot like no player at Southgate’s disposal and Kevin de Bruyne may be his only superior in this regard in the Premier League.
He set up at least five chances for team-mates that could and sometimes definitely should have been taken advantage of.
Even if he is not the preferred option for right back, there is no better player to come on as a plan B when required to create a goalscoring opportunity.
Liverpool: Alisson 6; Alexander-Arnold 8*, Phillips 7, Kabak 7, Robertson 7; Fabinho 7, Wijnaldum 7, Milner 7; Salah 6, Mane 7, Firmino 6.
Subs: Jota 6, Thiago 7, Oxlade-Chamberlain 7, Shaqiri 6.
Real Madrid: Courtois 7; Valverde 7, Militao 7, Nacho 8, Mendy 7; Casemiro 8, Kroos 6, Modric 7; Asensio 7, Vinicius 7, Benzema 6.
Subs: Rodrigo 6, Odriozola 6, Isco 6.
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3' Long ball down the middle finds Mane behind the defence, he squares to Salah and his effort was saved by Courtois' legs. What a chance.
20' Off the post! Benzema nicks the ball off Phillips and then teases Kabak before hitting a cross that deflected off the Reds defender and hits the near post.
41' Lovely turn from Wijnaldum, then a good pass for Mane who squares to Salah but he fires over the bar.
81' Great chance for Benzema who is found unmarked in the centre by Militao but heads against the floor and it bounces over the bar.
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