Leicester fought hard to overturn the 1-0 deficit they suffered last week at Vicente Calderon but ultimately fell short.
Saul's goal for the visitors after just 26 minutes meant Craig Shakespeare's men were left with a mountain to climb at the King Power Stadium.
Despite Jamie Vardy's equaliser and late pressure, the Foxes were unable to undo the damage caused by Atletico's early away goal and the tie ended 1-1 - with Atletico progressing through 2-1 on aggregate.
Here, Sportsmail's LAURIE WHITWELL runs the rule over the performances of both sets of players.
LEICESTER (4-4-1-1)
Kasper Schmeichel 6.