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The Ghanaian international was given a starting berth by Diego Simeone at the heart of the midfield alongside Saul Niguez.
Substitute Borja Garcia's shot fired in off Seydou Doumbia in the 88th minute to undo Antoine Griezmann's inspirational rescue act and hand Diego Simeone's men a heart-breaking exit from a tournament they last won in 2013.
Griezmann, introduced on the hour, had only moments previously completed a quickfire Atletico comeback by lashing them into the lead after helping Angel Correa level the scores inside 90 minutes.
But Girona - who earlier overturned Nikola Kalinic's first-half opener thanks to goals from Valery Fernandez and Cristhian Stuani - recovered to incredibly snatch back the ascendancy as a 4-4 aggregate draw saw them through.
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Partey featured in the first leg clash which ended 1-1 last week.
He has made 23 appearances in all competitions, scoring two goals.