Liverpool exited the Champions League with a 6-2 aggregate defeat to Real Madrid as Karim Benzema's late strike condemned the Reds to a 1-0 loss in the second leg.
Liverpool's capitulation at Anfield had left them needing another miraculous European comeback to reach the last eight but it did not materialise at the Bernabeu, the reigning champions ramming home their advantage with Benzema's close-range strike (78).
Darwin Nunez went closest for Jurgen Klopp's side in an entertaining first half when he was twice denied by Thibaut Courtois, but Liverpool were indebted to their own goalkeeper, Alisson, for keeping Madrid at bay with a series of saves before their goal.
Madrid, winners over Liverpool by the same scoreline in last year's final, will now aim to go on and lift the trophy for the 15th time, leaving Klopp's men with a top-four finish in the Premier League as their sole remaining target in a bitterly disappointing season.
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How Liverpool's defeat unfolded
Klopp threw caution to the wind with his starting line-up, including an additional forward in Diogo Jota, so it was hardly surprising that, at the other end, Real Madrid found space to attack early on.
The first chance fell to Liverpool, with Courtois denying Nunez after Mohamed Salah had got the better of Antonio Rudiger, but a succession of Madrid opportunities followed.
Benzema and Vinicius Junior, the pair that so terrorised Liverpool in the first leg, threatened an opener when the latter's cut-back just eluded his team-mate, and the visitors needed their goalkeeper to save them soon after that.
Alisson's point-blank stop from Vinicius was outstanding, and he rescued Liverpool again when he acrobatically tipped a long-range effort from Eduardo Camavinga onto the crossbar.
Luka Modric sent another powerful strike from distance narrowly over but Liverpool soon started to grow into the game, with Nunez and Cody Gakpo spurning headed opportunities before the former drew a fine one-handed save from Courtois with a curling effort.
Vinicius remained a threat up against Trent Alexander-Arnold but Liverpool went close again when Gakpo's stinging shot from the right-hand corner of the box had to be pushed around the post by Courtois.
Madrid's experience told in the second half, however, as the wily hosts negated Liverpool's attacking threat and controlled the game, with the evergreen Luka Modric at the heart of things.
Federico Valverde was denied by Alisson in a one-on-one soon after half-time and more Madrid chances followed, with Valverde again going close when he headed a Modric cross over, and Benzema blasting a shot into the stands from a Vinicius centre.
It appeared Liverpool might at least claim a draw after that uncharacteristic miss from Benzema, but the Frenchman made no mistake when Vinicius failed to connect with his shot following a ball over the top, instead sticking out a leg to set up his team-mate.
There was a lengthy VAR check for a Madrid penalty in stoppage time, prolonging a disappointing evening for the visitors, but the referee decided not to penalise substitute Kostas Tsimikas for handball after consulting the pitchside monitor.
After full-time, there was a sympathetic gesture for those who had travelled from Merseyside, with You'll Never Walk Alone played out over the stadium speakers at the Bernabeu. It made for a poignant end to Liverpool's European campaign.
Klopp: We couldn't put in a special performance
Liverpool boss Jurgen Klopp to BT Sport: "Being 5-2 down is obviously not a great result and if you want to go through, you need to have a really special performance, and we couldn't put a special performance on the pitch tonight.
"It was an open game but Madrid had better chances. Alli (Alisson) had to make two sensational saves. In the end, the goal is a scrappy one but that's obviously not decisive anymore.
"The right team went through that's what we have to admit. Madrid controlled the game, we gave them the opportunity to control it. Knock-out stages are like this, there's probably 500,000 different ways to go out, this was ours tonight. It's not what we wanted but it's what we got. Now we have to carry on.
"You need moments. If we were to score in the first half it could give the extra spark but that is hypothetical, we will not know. Madrid were the better team and won the game. In three halves of the games they were the better team, that's how you go through to the next round.
"If you draw at home and play the game we played tonight then we go out probably as well. We can't come here and hope you get something. We prepared for a special performance but we were not able to put it on the pitch tonight. It was obvious the best side went through."
Madrid haunt Reds again - Opta stats
- Real Madrid have now eliminated Liverpool from the Champions League in each of the last three seasons (2020-21 quarter-final, 2021-22 final, 2022-23 last-16). It's just the second time that a side has been eliminated in three consecutive seasons all by the same opponent, after Atletico Madrid, also by Real Madrid (run of four from 2013-14 to 2016-17).
- Real Madrid have qualified for their 19th Champions League quarter-final, with only Bayern Munich (21, including 2022-23) reaching more. Real Madrid have now moved one ahead of Spanish rivals Barcelona (18).
- Liverpool's 6-2 aggregate loss to Real Madrid is their heaviest margin of defeat over two legs of a Champions League tie.
- Under Jürgen Klopp, all six of Liverpool's eliminations from major European competitions have come against Spanish clubs (Sevilla x1, Atletico Madrid x1, Real Madrid x4).
- Real Madrid's Karim Benzema has scored seven Champions League goals against Liverpool, the most of any player. Indeed, only Lionel Messi (27) has more goals against English clubs overall in the competition than the Frenchman (19).
What's next for Liverpool?
Liverpool's next game is not until after the international break, on Saturday April 1, when they face Manchester City in the Premier League, kicking off at 12.30pm.
Their scheduled meeting with Fulham this weekend was postponed due to the Cottagers' participation in the FA Cup.
When is the draw?
The draws for the Champions League quarter-finals and semi-finals take place at 11am UK time on Friday, March 17 in Nyon, Switzerland at UEFA's headquarters.
The eight last-16 winners are involved in an open quarter-final and semi-final draw.
There are no seedings and no country protection, so clubs can face opposition from the same country. They can also draw teams they previously played in the group stage.
A final draw will also take place to determine the 'home' side for administrative reasons for the showpiece event in Istanbul, Turkey on June 10.
You can follow the draw with Sky Sports' live blog, so you can keep across everything right here.