Gorka Guruzeta struck both goals for Athletic.
Valverde said: "I enjoyed when it was over, but before I was very involved because they could score. It was a game in which we did not start with fluidity and it was difficult for us. They had a chance with Guridi and the penalty that Unai saved. The next play marked the game.
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"What worries me most is that those who leave return (in international week) without problems. The team's dynamics will not be cut off by the break and the whirlwind of the Cup continues its course."
On Guruzeta, he added: "He hasn't surprised me, but you can ask him for more because I ask him for it. He's different from other scorers we've had. Guruzeta scores goals and comes into play, which makes him better and more focused."