Diego Simeone's men have been handed a potentially difficult route to the final, facing the possibility of a second-round clash against Valencia and a semi-final meeting with city rivals Real Madrid, in what would be a repeat of last season's final.
Atletico came out on top on that occasion, as Miranda's extra-time strike secured a 2-1 triumph.
The draw has also thrown up the potential of a meeting in the final for El 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 La Liga champions Barcelona face off with Cartagena.
Gerardo Martino will be content with Barcelona'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 ib Athletic Bilbao, and Valladolid and Rayo Vallecano will go head-to-head.
Other notable fixtures see potential banana skins for Sevilla and Valencia, the former open against Racing Santander, while the latter face an encounter with Gimnastic.
The first leg of round one will take place on December 7 and 8.
Draw in full: Real Valladolid v Rayo Vallecano, Huelva v Levante, Cartagena v Barcelona, Girona v Getafe, Algeciras v Real Sociedad, VIllarreal v Elche, Las Palmas v Almeria, Racing Santander v Sevilla, Alcorcon v Granada, Real Jaen v Espanyol, Olimpic Xativa v Real Madrid, Malaga v Osasuna, Gimnastic v Valencia, Sant Andreu v Atletico Madrid, Lleida v Real Betis, Celta Vigo v Athletic Bilbao.
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