The Reds went to the Santiago Bernabeu 5-2 down on aggregate following the first-leg of their round of 16 tie and therefore in need of a miracle to progress to the quarter-finals.
Liverpool, known for their remarkable comebacks from three goals down in the Champions League, hoped to conjure some of the magic from the wins against AC Milan and Barcelona to defeat the club that beat them in last year’s final.
But Jurgen Klopp’s team looked far from their best and devoid of ideas in Spain, with a late goal from Karim Benzema consigning them to an early exit from the competition.
It was a lively first-half as both sides threw caution to the wind, with Darwin Nunez testing Thibaut Courtois after just seven minutes.
Real began to dominate proceedings, with Alisson making a miraculous save to deny Vinicius Jr. from close range before tipping Eduardo Camavinga’s deflected shot onto the crossbar.
Just minutes later Luka Modric came very close to putting the tie to bed but his powerful effort was just too high.
Liverpool worked their way back into the game shortly after, with Courtois making two fine saves to deny Nunez and Cody Gakpo.
But after the break, the Reds failed to create anything of note as they failed to breakdown a well-organised Real side who continued to press for a goal with Benzema and Federico Valverde both missing from close range.
Eventually, with just over 10 minutes to go, the ball did find the back of the net through Benzema tapping home after Vinicius managed to flick the ball into his captain’s path.
It was the Ballon d’Or winner’s 89th Champions League goal, though it came at a cost with the striker injurying himself in the process – just days before Real are set to play arch-rivals Barcelona.
As for Liverpool, the Champions League was their final shot at winning a major trophy this season and now the best they can hope for is finishing in the Premier League top four.
In Wednesday’s other game, Napoli reached the quarter-final stage for the first time in their history after beating Frankfurt 3-0 (5-0 on aggregate).