The match, which is played between the two best performing Basque sides from the previous season's LaLiga derbies, took place at Barakaldo's Lasesarre stadium.
"These derbies are never friendly," Valverde said post-match. "There was intensity and it was an interesting match in every respect. I think we gave it our all and so did they.
"I liked the fact that we always tried to take the initiative and that we showed a lot of fight in the game."
Beyond the results in these warm-up matches, the Athletic head coach is focused on his team being in the best possible shape for their return to competitive action.
He said: "What I want is to win the first league game. This match was very good because it was a learning experience and a way of seeing where we're at, so it was a good test in that sense."