Saul Niguez's opening goal made the task all the more hard for Leicester, who by then required three goals to overturn the deficit.
Saul's header proved crucial though as Diego Simeone's side - beaten finalists in two of the last three years - squeezed into the semi-finals in search of their maiden Champions League crown.
But Leicester came out fighting in the second half and Jamie Vardy's strike with half an hour remaining gave the Premier League champions hope.
Atletico Madrid's Gabi, right, and Koke, 6, celebrate after the Champions League quarterfinal second leg soccer match between Leicester City and Atletico Madrid at King Power Stadium, Leicester, England, Tuesday, April 18, 2017.
But despite sending on Leonardo Ulloa for Shinji Okazaki at half-time and leading the shot count 17-2 after the break, they were unable to breach a resolute Atletico defence for a second time.
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"We can leave the competition with our heads held high", said Leicester City captain Wes Morgan.
"The Champions League was a new experience for most of us, we definitely enjoyed it. But after two years of pulling off football miracle after football miracle, they met their match in Atletico Madrid".
"I believe they've been unlucky in the previous couple of years and we are able to begin to see the quality they've in both games. We lived in fear all night".
Cristiano Ronaldo on Tuesday scored a hat-trick to send Spanish giants Real Madrid through to the Champions League semi-finals with a 4-2 extra-time win against 10-men Bayern Munich. "It's in the club's hands, I've said we'd sit down at the end of the season, I'm more than happy to do that before if it arises but the contract says until the end of the season", he said. Their league form may have dipped this season, but they appear as risky as ever as they head into the semi finals.
Leicester did a phenomenal job to get this far.
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As in their victories on home soil versus against Porto, Copenhagen, Club Brugge and Sevilla, the Foxes provided a reminder of the irresistible qualities and belief that propelled them to the Premier League title last season.
"If we had shown the same form all season that we've shown of late, we could be in a Champions League spot again".
Speaking after the game, the Argentine boss said: "I'm full of emotions, full of pride for the performance of my team".
I also have to say, what a great performance from our opponents.
Jamie Vardy does what he always seems to do, and poached a goal in the 61 minute to give Leicester hope of writing another chapter in that fairytale, but it was not to be.
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"We felt we could get back into it and we created chances but they were blocked, " said Drinkwater's central midfield partner Wilfred Ndidi, who feels the Foxes can get back into Europe.