Craig Shakespeare's side came into the second leg at the King Power Stadium trailing 1-0 in the tie following Antoine Griezmann's controversial penalty a week earlier.
But things went from bad to worse for the Foxes when former Chelsea left-back Filipe Luis delivered a pinpoint cross into the box for Saul Niguez who met the ball on the run with a strong header that hurtled its way into the bottom corner of the net in the 26th minute.
The goal meant Leicester needed three to progress to the semi-finals, and they proceeded to up their tempo and were duly rewarded just after the hour mark.
Jamie Vardy was the goalscorer after poking in from eight yards to hand hope to Leicester in the 61st minute. But Atletico - famed for their solid defence - held firm to book their place in the last four of the Champions League for the third time in four seasons.
In contrast, the result brought to an end Leicester's fairytale in Europe's premier competition after the Foxes had become the first team since Malaga in 2012-13 to make it to the quarter-finals of the Champions League on their debut.
They reached this stage by seeing off Sevilla 3-2 on aggregate in the round of 16 after finishing top of Group G with 13 points, two more than second-placed Porto.
The team currently sit in 12th place in the Premier League table and are unlikely to secure Champions League qualification for next season, as they did last May when they stormed to an unexpected top-flight title.