Diego Simeone's men have been handed a difficult route to the final, facing the possibility of a second-round clash against Valencia, as well as a potential semi-final showdown with city rivals Real Madrid, whom they defeated in last season's tournament decider.
Atletico, of course, came out on top on that occasion, as Miranda's extra-time strike secured a 2-1 triumph for the Rojiblancos.
The draw has also thrown up the potential for a final meeting between Clasico rivals Real Madrid and Barcelona, with the Liga giants on opposite halves of the draw.
First up for Carlo Ancelotti's charges will be second-tier outfit Olimpic Xativa, while reigning Primera Division champions Barca face off with Cartagena.
Gerardo Martino will be content with Blaugrana's draw, although they could meet Villarreal, Real Sociedad or Sevilla in the final four.
The first round has provided four all top-flight fixtures: Villarreal and Malaga face Elche and Osasuna, respectively, Celta Vigo take on Athletic Bilbao, and Valladolid and Rayo Vallecano will go head to head.
Other notable fixtures see potential banana skins for Sevilla and Valencia, as the former open against Racing Santander, while the latter face an encounter with Gimnastic.
Round one's first legs will take place on December 7/8.