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.
Trailing 3-1 from last week's first leg, 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.
- Analysis: Liverpool's big challenge now
- Jurgen Klopp: We must get back in CL
- Police launch probe as Real Madrid's team bus targeted at Anfield
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 Sky Sports on Monday Night Football.
- How the teams lined up | Match stats
- Champions League semi-final draw
- Champions League news | Fixtures | Results
Semi-final draw
First legs: April 27/28 | Second legs: May 4/5
- Paris Saint-Germain vs Manchester City
- Real Madrid vs Chelsea
How Liverpool's Champions League dreams ended...
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.
What the managers said...
Liverpool boss Jurgen Klopp: "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 Zinedine Zidane: "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."
'We need to put this disappointment behind us'
Liverpool midfielder James Milner to BT Sport:
"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."
Opta stats - Liverpool's struggles against Spanish sides continue
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.
What's next?
Liverpool travel to Leeds in the Premier League on Monday Night Football at 8pm, live on Sky Sports Premier League from 7pm.
Meanwhile, Real Madrid are back in La Liga action on Sunday when they face Getafe; kick-off 8pm.