Real Madrid held on to their first leg lead to cement their place in the Champions League semi-final.
Liverpool could've made the tie slightly more interesting had Mohamed Salah found the back of the net inside two minutes but Thibaut Courtois was alert and saved well.
Zinedine Zidane's side fought and hung on for their dear lives in stages, but maintained the two-goal lead from the first leg.
Jurgen Klopp's side ultimately made to regret their showing in Madrid and failure to hit the back of the net as opportunities went begging.
Liverpool ruing wasted opportunities
Liverpool left the starting blocks with the intensity and desire that struck fear into the opposition, they had the lion share of the chances that occurred in the opening 45 in what was performance fans have been accustomed to.
It was almost a dream start for Liverpool inside the opening minute, Sadio Mane and Salah combined but the Egyptian was denied by the feet of Thibaut Courtois.
James Milner then forced Courtois into a brilliant save to claw his effort out of the top corner.
Real Madrid came close themselves, Karim Benzema cut onto his left foot, his effort was then deflected onto the post.
The final pass or finish let Liverpool down when they needed it most. Jurgen Klopp's side looked dangerous but failed to create a clear sight on goal. Two in a matter of minutes fell to the hosts through Mohamed Salah and Georginio Wijnaldum both times they failed to keep it down.
Real Madrid held on in what was an encouraging half for Liverpool, but the Reds, in what was their best half of football all season, failed to make chances pay and their efforts to break the deadlock fruitless.
1: Promising start from Salah, good combination play with Mane
SALAH?!?! Needs to score
Probably the best five minutes of Liverpool's season.
Real Madrid still threatening whenever they have possession.
Great effort from Milner.
Can't allow Benzema that much space and get a shot off
Final ball killing the Reds.
Three outstanding opportunities but failing to keep them down or get them on target.
Real Madrid killing the game keeping possession and running the clock down in the final stages of the first half.
Real Madrid hold on
Inside 50 seconds, Firmino spun his marker only to fire straight at Courtois.
Liverpool's Brazilian forward had two sights on goal following his early chance, his first a header which didn't trouble before his left-footed effort sailed over the bar.
With half an hour remaining, Jurgen Klopp made the bold call of bringing on Thiago and Diogo Jota forcing Fabinho into the back four.
Real Madrid had their rare sight of goal in the second half, Vinicius Jnr was set off by Fede Valverde but Alisson was alert and brave on two occasions as Benzema steamed in for the rebound.
It wouldn't go in for Liverpool. Every eye on goal they got, a Real Madrid shirt was flying in front of the effort to thwart the danger. Substitute Jota, worked well through the Madrid defence but fired into the side netting.
Benzema had a chance go begging, his free-header went into the ground and over the bar.
But the 13-time winners held on as it was the same old story for Liverpool when it came to the final third.
Liverpool starting bright again
Firmino failing to test Courtois on two occasions, the best chance coming immediately after half-time.
Great goalkeeping from Alisson on Vinicius and Benzema
It was like the story of Liverpool's season where they couldn't get the rub of the green, every Real Madrid player throwing themselves in front of the Reds desperate attempts on goal.
Despite a positive showing from the Reds, they ultimately failed to hit the back of the net and it cost them dearly.
It just wasn't to be.
LFC Transfer Room Verdict
Gutted, disheartening, there aren't many other words to describe it. It was there for the taking.
At the end of the day, it's a game of two legs in this knockout structure and Liverpool were made to pay for their horrific first-half display.
Those wrongs could've very well been written as the Reds had a catalogue of chances to even win the fixture on the night.
Over the course of 90 minutes, it was the Liverpool of old only lacking the cutting edge that made the world-class teams look minuscule.
However, poor finishing cost Klopp's side from the first minute, as Mohamed Salah was denied by the outstretched leg of Thibaut Courtois to the last with many openings in between.
You can't help but think what could've been, a game of if's and what could have been's for the Reds in their pursuit of number seven.
It was an uphill task from the first blow of Björn Kuipers whistle, despite flying out of the blocks, Liverpool couldn't keep the ball down or hit the back of the net.
Some positives can be drawn as an energetic, eager and ferocious Liverpool came to the fore once again but failing to make chances count and 75 minutes of what can only be described as cowardly play in the first leg made a tough task, gigantic.
The relief on the faces of the Real Madrid players illustrated they were in for a game and that on another day by half-time or even the hour mark they could've been out of sight.
Sadly it wasn't to be for Liverpool and you can't fault the effort but now all their focus goes on ensuring they don't miss out on the grandest stage of European football.
Liverpool v Real Madrid - Match Facts:
Liverpool: Alisson, Alexander-Arnold, Phillips, Kabak, Robertson, Milner, Fabinho, Wijnaldum, Salah, Firmino, Mane.
Real Madrid: Courtois, Valverde, Eder Militao, Nacho, Mendy, Modric, Casemiro, Kroos, Asensio, Benzema, Vinicius Junior.
Bookings: 25' Robertson, 59' Phillips; 25' Casemiro
Subs: 60' Thiago & Jota (on for Milner & Kabak) 82' Oxlade-Chamberlain & Shaqiri (on for Firmino & Mane), 72' Rodrygo & Ordiozola (on for Vincius & Kroos), 82' Isco (on for Asensio)