Goals from Antoine Griezmann, Oscar de Marcos and Asier Villalibre ensured both Barcelona and Athletic Bilbao played 2-2 after 90 minutes and forced an extra 30 minutes.
However, Inaki Williams’s brilliant strike in extra-time gave Athletic the victory over Koeman’s men at Seville’s La Cartuja stadium, as Lionel Messi was sent off in the final stages.
“You have to analyze the game. It’s difficult. We are sad and disappointed because we wanted to win,” Koeman was quoted by Mundo Deportivo as saying after the game.
“It’s not a step backwards. A title is convenient to show that you’re on the right path, but we have still shown that we are.
“We have done everything to win, but we were very tired. For many players, it will prove a good experience to have played in this final.”
Barcelona’s next match is against Cornella in the Copa del Rey on Thursday.