Winning the first leg 1-0, Atletico were their typically efficient selves with Saul Niguez's header rendering Jamie Vardy's goal just after the hour mark inconsequential.
While struggling in the Premier League after their shock triumph last season, the Foxes form in the UCL has been strong, rarely succumbing against more highly fancied opposition, but needing two goals against Diego Simeone's defensively disciplined side ultimately proved too much to handle.
Leicester had won all four of their home games in the Champions League, conceding only goal in the process with with a vehement crowd getting behind their side who failed to register a shot on target at the Vicente Calderon in the first leg, with Shinzi Okazaki's effort from a Vardy cutback continuing the theme.
Without the suspended Robert Huth, the hosts defensive frailties that had hindered them for so much of the Premier League season reappeared midway through the opening period with Filipe Luis delivering a well-placed cross that found Saul in space whose well-placed header went beyond Kasper Schmeichel's grasp.
Needing a quick response, Riyad Mahrez's deflected volley called Jan Oblak into action but the hosts otherwise offered little else in attack before the break as Craig Shakespeare brought on Ben Chilwell and Leonardo Ulloa for Yohan Benalouane and Shinji Okazaki during the interval.
Chilwell was in the thick of things as he fired a shot just over the crossbar from inside the box, while at the other end Marc Albrighton's defensive effort was enough to stop Yannick Carrasco from latching onto Antoine Griezmann's square pass that would have surely led to Atletico's second.
Leicester's hopes were kept alive when Vardy side-footed in from six yards after Chilwell's shot was blocked in the 61st minute before Vardy and Ulloa were both denied in quick succession by Atletico defending as the Foxes grew in confidence as Simeone's side dug their heels in.
Mahrez came close with a swinging free-kick in the 76th minute as it continued to be one-way traffic, but time ultimately ebbed away for Leicester who bid farewell to a European stage they may not see again for a long time.