The reigning champions, Real Madrid, put the kibosh on Liverpool's heroic comeback attempt, emerging from Wednesday night's contest with a 1-0 victory to progress to the Champions League quarterfinals.
Genuine, the record 14-time champions, had already secured a historic European home win over Liverpool three weeks ago at Anfield with a 5-2 triumph from being 2-0 down.
During their 300th Champions League match at the Bernabeu, Karim Benzema's late winner clinched a 6-2 aggregate success for Real.
Despite their performance in the first leg, both goalkeepers Thibaut Courtois of Real and Alisson Becker of Liverpool were almost unbeatable at the Bernabeu.
Courtois was particularly frustrating for Liverpool, as he had been in last year's final, which Real won 1-0.
Liverpool attempted to fight back from their historic first-leg defeat, but Courtois made another save against Darwin Nunez's curling shot and palmed away a cannon from Cody Gakpo.
At the other end, Vinicius Junior was denied from point-blank range by Alisson, who also managed to tip a long-distance drive from Eduardo Camavinga against the crossbar.
Federico Valverde was the next player denied by Alisson after the restart. Still, eventually, Real broke the deadlock in the 79th minute when Benzema slotted into the empty net after Vinicius Junior had flicked the ball over to him past Alisson while lying on the ground.
Liverpool left with their anthem, "You'll never walk alone," played in the Bernabeu as manager Jurgen Klopp admitted it was not a performance for a miracle.
"Real Madrid was the better team. The right team went through. If you want a miracle, you must play better or against another team," he said.
Meanwhile, Italy's Napoli reached the quarterfinals for the first time by completing a comprehensive 5-0 overall win over Europa League champions Eintracht Frankfurt with a 3-0 home victory from Victor Osimhen's brace and Piotr Zielinski.
Napoli's success means that Italy has three teams in the final eight for the first time since 2006, with AC and Inter Milan being the others.
Serie A clubs have not lifted the trophy since Inter's success in 2010.
The game in Naples was overshadowed by fan violence in the city center in the afternoon, according to reports from both camps, as hundreds of Frankfurt fans had made their way to Italy despite a blanket stadium ban on Frankfurt residents imposed by the local prefecture over security concerns in connection with violence three weeks ago at the first game in Germany.
On the pitch, Matteo Politano had the first chance for the runaway Serie A leaders two minutes into the game. Frankfurt goalkeeper Kevin Trapp then saved twice from Khvicha Kvaratskhelia.
Frankfurt rarely threatened, and their comeback hopes ended in first-half stoppage time when Osimhen rose to head Politano's cross into the top right corner.
Captain Giovanni di Lorenzo's cross was poked home by Osimhen in the 53rd, and Zielinski converted a penalty 11 minutes later after being brought down by Djibril Sow.
"It wasn't easy, but we managed to reach a historical aim for Napoli," Napoli coach Luciano Spalletti told UEFA.com.
Frankfurt midfielder Sebastian Rode conceded to streaming portal DAZN that "we have lost again against a fantastic team, they have a lot of class, everyone knows their part. We did well over long courses but gave the ball away badly for the goals."
England's Manchester City and Chelsea, Germany's Bayern Munich, Portugal's Benfica and Spain's Real are the other teams, with the quarter and semifinal draw scheduled for Friday.
