Having claimed a 1-0 first-leg triumph courtesy of Antoine Griezmann's controversial penalty, Diego Simeone's side were typically efficient in Tuesday's return leg - Saul Niguez's first-half header rendering Jamie Vardy's goal immaterial.
As shock Premier League champions last season, the Foxes have rarely wilted in the face of improbable odds, but the requirement of another two goals against a side so tactically astute and defensively disciplined proved beyond Craig Shakespeare's men.
Leicester had won all four home games in this season's Champions League, conceding only once in the process, and they tried gamely to protect that proud record, with a vociferous crowd treated to a spirited showing.
But, having switched off in defence to allow Saul to nod in a crucial away goal after 26 minutes, Vardy's close-range finish proved their only tangible reward for a resilient second-half performance that merited at least a win on the night.
1 - Jamie Vardy is the first English player to score in a Champions League quarter-final since Frank Lampard in 2012. Party.— OptaJoe (@OptaJoe) April 18, 2017
That Vardy strike give them an opportunity to apply some pressure in the remaining half an hour - and they certainly did that - but Simeone's well-drilled charges once again proved well equipped to cope with being on the back foot, keeping their bid for Europe's top prize alive and kicking.
Leicester, meanwhile, will go back to a league campaign that looks certain to end in safety and can reflect on a remarkable journey on the day that marked eight years since they were crowned champions of the third tier.
The Foxes - who overcame a 1-0 first-leg deficit to get past Sevilla in the previous round - did not register a shot on target at the Vicente Calderon and Shinji Okazaki's wayward effort from Vardy's cutback continued that theme.
Although they were without the suspended Robert Huth, the hosts had Wes Morgan back from injury, but the defensive frailties that had so frequently hindered them this season under Claudio Ranieri reappeared midway through the opening half.
Filipe Luis had time to deliver a cross from the left, finding Saul in space to steer a measured header beyond Kasper Schmeichel's despairing dive for his sixth Champions League goal.
Leicester needed a swift response and Riyad Mahrez's deflected volley called Jan Oblak into action, but the Foxes offered little else in attack before the break.
Shakespeare made a double change at the interval, bringing on Ben Chilwell and Leonardo Ulloa for Yohan Benalouane and Okazaki.
Chilwell was quickly into the action, firing narrowly over the crossbar from inside the box, while at the other end Marc Albrighton did enough to prevent Yannick Carrasco getting on the end of Griezmann's square pass.
The home side were given a glimmer of hope when Vardy side-footed in from six yards after Chilwell's shot had been blocked in the 61st minute.
Ulloa and Vardy were denied in quick succession by heroic Atletico defending as Leicester visibly grew in confidence, while the visitors dug their heels in.
A swinging free-kick from Mahrez only just cleared the bar in the 76th minute as it continued to be one-way traffic, but time ebbed away for Leicester, who waved farewell to a stage they may not grace again for a long time.
Key Opta facts:
- Atletico Madrid have qualified in the three Champions League knockout rounds in which they won 1-0 in the first leg under Diego Simeone.
- Saul Niguez scored Atletico Madrid's 100th goal in the Champions League.
- Saul has scored more goals than any other player in Champions League since the beginning of the last season (6).
- With Atletico qualified, there will be at least one Spanish side in Champions League semi-finals for the 10th season in a row.