They have reached their third semi-final in four years but boss Diego Simeone admitted the Rojiblancos survived a major scare.
Saul Niguez's first-half header gave the visitors an away goal and put the tie out of Leicester's reach despite Jamie Vardy's second-half equaliser.
Leicester's stirring run to the quarter-finals came to an end on Tuesday as Atletico Madrid held out for a 1-1 draw and a 2-1 aggregate triumph at a raucous King Power Stadium.
Leicester's already hard task now took on Everest-like proportions as they were required to score three goals against a mean defence, who had leaked only four so far in the competition.
Leicester's Jamie Vardy's 61st-minute goal cancelled out Niguez's 26th-minute strike in the second leg of the quarter-final on Tuesday night but Atletico's 1-0 win plus an away goal here gave them a comfortable 2-1 win. They should want more of this. We had them rattled at times and it's no discredit to lose to a team of that calibre.
"I've just said to them that they should want more of this and they've agreed to a man that that's what they want".
Vardy, whose goals propelled Leicester to the most unlikely of Premier League titles last season - a year after the club narrowly avoided relegation - has rediscovered his fire after a post-title funk that cost manager Claudio Ranieri his job.
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A return to Europe is off the agenda this season, as Leicester lie 12th - 20 points shy of seventh-placed Everton.
Atlético have now scuppered Leicester's hopes in three of their four European campaigns to date, knocking them out of the first round of the 1961-62 Cup Winners' Cup and the 1997-98 Uefa Cup.
"I feel emotion, pride and hope after such a tough game against a team which gave us so much pleasure to compete against, a team that did not throw in the towel and kept us at arms' length", said Simeone.
Atletico looked like they could pick Leicester off at will as they kept the ball and nearly killed the tie with Griezmann's exceptional work rate underpinning their performance.
They defended with their customary tenacity, while two unsafe crosses from Yannick Carrasco - preferred up front to the fit-again Kevin Gameiro - demonstrated their threat on the counter.
But Leicester coach Craig Shakespeare began the second half by making a double substitution: Leonardo Ulloa for Okazaki and Ben Chilwell for Yohan Benalouane.
A draw at the King Power stadium was not enough to see the Foxes progress through to the latter stages of the prestigious tournament, with Atletico having won the first leg courtesy of a controversial penalty decision.
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