Karim Benzema scored the only goal as Real Madrid beat Liverpool 1-0 to progress comfortably to the Champions League quarter-finals.
The Reds needed to score three without reply to have any chance of progression as a result of losing the first-leg 5-2 at Anfield after a second-half implosion.
However, they failed to impose themselves on the hosts and hardly tested Thibaut Courtois as their European campaign came to a miserable end.
Los Blancos march on as they seek to win the competition for the fifteenth time and teams will be fearful of drawing the Spaniards.
Story of the Match
Carlo Ancelotti made two changes from the win against Espanyol at the weekend, with Benzema and Antonio Rudiger replacing Rodrygo and Aurelien Tchouameni.
The Reds were forced into a tactical switch to a 4-2-3-1, as Jurgen Klopp made two changes from their loss to Bournemouth, James Milner and Diogo Jota replacing Harvey Elliott and the injured Stefan Bajcetic, with skipper Jordan Henderson also ruled out through illness.
The visitors had an early warning as Benzema found himself through on goal in the third minute but he was offside by a considerable margin.
The Reds then had the first real chance of the contest, Darwin Nunez was played in by Mohamed Salah after a slip from Rudiger, but he couldn't generate enough power to beat Courtois seven minutes in.
Their blushes were saved by Milner at the other end, as he stopped Toni Kroos from latching onto a cut back after a poor Trent Alexander-Arnold pass had allowed the hosts to get in-behind.
Kroos then fired a long-range effort towards the visitor's goal but it was comfortable for Alisson despite a deflection.
Minutes later, the Brazilian pulled off a stunning save to deny his compatriot Vinicius Jr from close range at the back post after the ball was headed across the box.
Liverpool then got into a very dangerous area but Jota made a meal of the chance after a cut back from Salah.
The hosts then attempted to consolidate their aggregate lead, Eduardo Camavinga released a stunning long range effort with his left foot but Alisson somehow tipped it onto the crossbar.
Luca Modric then came inches from breaking the deadlock with a half-volley from range, the Reds keeper would not have had a chance had it been a little lower.
He then saved from Vinicius again after the tricky winger had taken the ball past Konate, but was ruled offside.
The Reds came back again, Cody Gakpo glanced a header wide after Alexander-Arnold had found him then Nunez headed straight at Courtois from a lofted Fabinho pass.
The Uruguayan then tested the Belgian with a powerful curling effort from a tight angle before Konate blasted over from the resulting corner.
Vinicius then hit a tame effort from a similar angle at the other end, straight into the arms of the visiting keeper.
As the half was coming to an end, Gakpo smashed a shot from just inside the area, but it was a nice height for Courtois as he pushed it out for a corner which came to nothing.
After the interval, the first real opportunity was when Vinicius nearly found Benzema but Virgil Van Dijk intercepted as the Frenchmen was about the tap the ball in, but it was ruled offside.
Alisson then saved a one-on-one from close range from Federico Valverde before Salah failed to find Nunez with a poor pass when the forward was in acres of space.
Vincius was causing the visitors all sorts of problems, but Alexander-Arnold made a great challenge to stop Benzema from scoring before the flag was raised again.
Roberto Firmino and Elliott replaced Jota and Nunez as Jurgen Klopp sought to add fresh impetus with the Reds still chasing the three-goal deficit.
Van Dijk then made two crucial interceptions stopping Valverde from finding two of his teammates unmarked in the box, before he stopped Nacho's cut back from finding the Frenchman.
Valverde then headed just over the bar from a Modric cross with Alisson rooted to his spot.
Benzema and Vinicius combined again, the Brazilian fizzing the ball into the Ballon d'Or winner, who could only blast the ball over.
The first booking of the match was for the Liverpool manager, as he complained a bit too aggressively over an alleged shirt pull on Salah.
Alex Oxlade-Chamberlain replaced Milner in the 73rd minute, as the visitors searched for a goal to give them hope.
The hosts put their progression beyond doubt in the 78th minute, Benzema tapped in when the ball fell to him after Vinicius poked it into his path.
The hosts then made a raft of changes with an eye to El Classico at the weekend, Dani Ceballos, Rodrygo, Marco Asensio and Tchouameni replacing Modric, Benzema, Vinicius and Kroos.
Lucas Vazquez then replaced Dani Carvajal for Madrid's final change as the game came to an end.
Fabio Carvalho and Kostas Tsmikas replaced Gakpo and Andy Robertson with two minutes remaining.
The Greek was involved in some controversy in the final stages as the ball bounced off his knee onto his arm in the box, leading to a rather ridiculous VAR check, but common sense prevailed and the referee did not give a penalty.
He received the only booking of the game for a player on the pitch, after a tangle with Ceballos.
The Liverpool keeper was arguably the only Reds player to come out of the contest with any credibility.
The Brazilian made a remarkable save from Vinicius which baffled the Madrid player and pundits as to how he had done it.
He then denied Camavinga from range with a fingertip save to keep to his side in with a chance in the first-half.
Another save from Valverde's close range effort in the early stages of the second-half kept his team in with a shout and he could not do anything about the goal.
One thing that is for sure about any potential rebuild at Anfield, Alisson has to stay in goal.