The Foxes dominated for much of the game at the King Power Stadium, creating numerous chances throughout, but were left with too much to do after Saul Niguez's 26th-minute header added to Atletico's one-goal advantage from the first leg in Madrid.
Needing three second half goals, Leicester responded with splendid defiance and equalised on the night when Jamie Vardy scored at the far post just after the hour.
They kept battling until the end as Atletico survived several scrambles, but the La Liga superpower held on and the Premier League's interest in the tournament ended.
Leicester City have gained huge credit and credibility in making their way to the last eight of the Champions League as England's last surviving representatives.
And even in defeat over two legs to this battle-hardened Atletico Madrid side - twice losing finalists in recent seasons - the Foxes can be proud of another monumental effort that just came up short.
Craig Shakespeare's side were second best as Atletico looked a cut above for the first 45 minutes to lead through Niguez's header, which left Leicester needing those three goals against a miserly defence.
The hosts could have been forgiven for throwing in the towel but instead came out fighting, invigorated by Shakespeare's positive half-time changes. He sent on Ben Chilwell and Leonardo Ulloa for Shinji Okazaki and defender Yohan Benalouane, flooding Vardy with greater support.
Vardy's goal was no more than they deserved and for a time they had Atletico rocking, giving the King Power Stadium belief that another miracle was on the cards. They almost added a second in goalmouth scrambles, especially when Stefan Savic blocked Vardy's goal-bound shot.
In the final reckoning, the lack of an away goal and a controversial first-leg penalty scored by Antoine Griezmann left them with a hurdle that was just too tough to surmount.
There was disappointment inside the King Power Stadium at the final whistle but it was masked by a fully deserved standing ovation for Leicester's players.
When last season's Premier League champions started their Champions League journey, many believed reaching the knockout phase would represent success - so once again they defied the odds. - BBC -