Liverpool's bid for a seventh Champions League title was ended as Real Madrid battled to a 0-0 draw at Anfield to secure a 3-1 aggregate win and a place in the semi-finals
, Jurgen Klopp's side knew they needed a fast start and that is exactly what they got, however, they spurned glorious chances with Mohamed Salah and Georginio Wijnaldum the guilty parties in the first half, while Thibaut Courtois had to be alert to keep out James Milner's long-range effort
Real Madrid were a constant threat on the break and they went close to a crucial away goal in the first half when Karim Benzema's deflected strike struck the foot of the post, but after the break Liverpool continued to press forward
However, they just could not find a way through the Spanish team's well-organised defence as their European dreams came to an end for another season
Victory over the two legs means Real Madrid, who are trying to win the competition for a 14th time, face another English test in the last four where they will meet Chelsea
Meanwhile, Liverpool's attentions now turn to trying to seal a place in next season's Champions League through a top-four finish in the Premier League, starting next Monday when they travel to Leeds, live on 
Liverpool raced out of the traps and a glorious opening fell to Salah in the third minute, but the Egypt forward's shot from just inside the penalty was straight at Courtois, who blocked the strike with his legs
Courtois was called into action again eight minutes later as Liverpool pinned back the visitors
 Salah played the ball into the path of Milner, who let fly from 25 yards, but Courtois leapt to his left to push the ball away from goal
Despite Liverpool's early dominance, Real Madrid almost grabbed a crucial away goal as Benzema's deflected shot beat the dive of Alisson, but luckily for the hosts, the ball rebounded off the foot of the post
Liverpool continued to play at a high intensity, and they finished the half the stronger of the two sides, creating two more big chances before half-time
 First, Salah shot over from inside the penalty area after being picked out by Sadio Mane before Wijnaldum lashed Trent Alexander-Arnold's cut back over the crossbar as Real got in at the interval unscathed
Attacking an empty Kop, Roberto Firmino forced Courtois into a smart block straight after the restart and powered a rising drive just over the crossbar moments later before Klopp turned to his bench
Liverpool brought on Diogo Jota and Thiago Alcantara as Klopp changed their shape to 4-2-3-1 with Salah promoted to central striker to allow the three other forwards to slot in behind him, with centre-back Ozan Kabak sacrificed as Fabinho dropped in from midfield
Real looked in control though as their defence sat back to soak up plenty of pressure from Liverpool, and they almost killed the tie off when Vinicius Junior broke down the left, the hosts requiring goalkeeper Alisson to block his shot and smother Benzema's follow-up
Liverpool still pressed forward and Thiago's cross-field ball was brilliantly kept alive by Alexander-Arnold only for Firmino's shot on the turn to rebound off Eder Militao when that vital breakthrough seemed likely
Benzema then should have put the hosts out of their misery when his downward header bounced over, but it mattered little with Liverpool's hopes of Champions League football now resting on overhauling Chelsea and West Ham, and perhaps even Leicester, to get into the top four
Liverpool boss : "You always need the key moments
 We didn't lose the tie tonight, we lost in Madrid
 It was uncomfortable for Madrid
 We were good, aggressive, had chances
 If and when is not interesting
 We didn't score and then the experience of Real Madrid played the tie down
 That is ourselves this year with the finishing
"We know how often Mo Salah finishes these things with closed eyes
 Not here
 Tonight it was absolutely okay, but we are out
 We love this competition and for other reasons it is very important we are back in it
 We can now concentrate on the Premier League and we will
 We have to work our socks off against Leeds
"Real Madrid boss : "We were up against it and we knew we had to suffer tonight, but in the end we got what we wanted, which was to go through
 I think we handled the game well, we rode the storm and can be proud of our display
"We knew they'd start fast and they were really good in the opening 15 minutes, but that's normal
 In the quarter-finals of the Champions League you have to dig in and we did that and got through
""I thought the performance was good
 The intensity, the desire was good, and we won the ball back well
 But you can't not take the chances we had tonight
 That was the difference unfortunately
"We wanted to come out of the blocks and make sure they had no time on the ball and set that tempo and intensity
 I think that carried through from early on
 It's disappointing because if we had played the first leg with that intensity it would have been a different story
"It's disappointing because we did everything, we wanted to do other than get the two goals which is obviously the most important thing"I think the most important thing is that we concentrate on our level of performance and if we perform with that intensity and desire and tempo that we played with tonight for the last league games then hopefully we can get into those top-four spots
"The most important thing is that we replicate this performance
 That's the one thing we've been missing, the consistency we haven't had, so that's what we need to get back and have a big push for the last few games and put this disappointment behind us
"Liverpool are winless in their last five games against Real Madrid in the UEFA Champions League (D1 L4), while they've failed to score in both games against them in this run at Anfield (0-3 in 2014-15 and 0-0 tonight)
Liverpool have only won one of their last 11 games against Spanish opponents in the UEFA Champions League (D3 L7), while failing to win any of their last four across the last two seasons (L2 v Atlético Madrid and D1 L1 v Real Madrid)
This was Liverpool's ninth two-legged knockout tie in the UEFA Champions League under Jürgen Klopp, and only the second time they have failed to win home and away in the tie (also versus Atlético de Madrid in the Last 16 in 2019-20)
Real Madrid have qualified for the semi-finals of the European Cup/UEFA Champions League for the 30th time, at least 10 more than any other team
Real Madrid have progressed from 11 of their 12 two-legged knockout ties in the UEFA Champions League under Zinedine Zidane, with their only elimination coming against Manchester City in last season's Last 16
Liverpool travel to Leeds in the Premier League on  at 8pm, live on  from 7pm
Meanwhile, Real Madrid are back in La Liga action on Sunday when they face Getafe; kick-off 8pm
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