A late Inaki Williams goal earned the victory for Bilbao.
"We had clear chances and played well," Bartomeu said. "We created a lot and I want to congratulate the players for how they played. They showed ambition and motivation. Now we have La Liga and the Champions League, Playing like that, I am sure success will follow.
"They had one shot on goal at the end and won the game. We deserved to go through, but it wasn't possible. I reiterate that I liked the ambition shown by the team on the pitch because it's a tough place to come and the home fans are on top of you.
"We are out of the Copa but now it's time to focus on La Liga and the Champions League. We're going to fight as we have done in this game."