Mohamed Salah and Georginio Wijnaldum were guilty of wasting glorious opportunities to get Jurgen Klopp’s men back into the tie as they failed to replicate a remarkable recovery from 3-0 down to beat Barcelona 4-3 on aggregate at the semi-final stage two years ago.
Madrid was far from their best but did not need to be to set up a semi-final clash with Chelsea as Los Blancos extended their unbeaten run in all competitions to 14 games.
Klopp admitted before the game that his players had to create their own atmosphere without the cauldron of noise that has accompanied famous European nights at Anfield in the past.
Despite the empty stands due to coronavirus restrictions, Liverpool flew out of the traps and should have halved their deficit within two minutes.
Sadio Mane knocked Ozan Kabak’s long ball perfectly into the path of Salah, but Liverpool’s one consistent performer in the final third this season fired straight at Thibaut Courtois.
Klopp surprisingly repeated his decision from the first leg to leave Thiago Alcantara on the bench with James Milner this time taking the place of the Spanish international in midfield.
Milner made his presence felt within a minute with a late lunge on Karim Benzema and nearly inflicted a different type of damage on Madrid 10 minutes in when his long range effort forced Courtois into another fine save.
Real’s fine run has propelled them back into contention to defend their La Liga title and claim a 14th crown as European champions.
However, Zinedine Zidane warned after Saturday’s 2-1 El Clasico win over Barcelona that his players were at their “physical limit” and the visitors looked jaded as they were happy to sit on their first leg lead.
The closest Madrid came to scoring was when Kabak inadvertently deflected a Benzema cross off the outside of his own post with Alisson Becker wrong-footed.
Chances continued to come and go for Liverpool as Salah snatched at another effort that flew high and wide.
Wijnaldum scored twice in the famous fightback against Barcelona in 2019.
However, the Dutch international was not as clinical against another Spanish giant as he blasted the best chance of the first-half over from close range.
Klopp went for it on the hour mark as Milner and Kabak made way for the introduction of Thiago and Diogo Jota.
Yet, even without three of their first-choice back four, Madrid was comfortable defending deep as Firmino, Salah, and Jota all had efforts blocked behind in quick succession.
Vinicius Junior’s double in the first leg proved to be the difference between the sides, but the Brazilian fluffed his one big chance to grab an away goal as Alisson smothered at his feet midway through the second half.
Benzema also should have done better when he mistimed a free header 10 minutes from time.
But a blistering first 45 minutes in the Spanish capital last week proved to be enough for Zidane to win a 14th of his 15 Champions League knockout ties in two spells as Madrid boss.