After the scores were level at 1-1, the final went to penalties, with Mallorca missing twice in the shootout to hand Athletic the triumph.
Aguirre later said: "The cruel thing about the end.
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"It happened to Real Sociedad not long ago. It's a coin toss and today it fell tails. I have nothing to reproach the players. We took Athletic to 120 minutes, a team that had beaten us the last time.
"We played a decent game. I don't have the face to scold them. It will be a long night, Real Madrid is coming on Saturday..."