Gorka Guruzeta, Nico Serrano and Robert Navarro struck the goals for Athletic in Bergamo.
Afterwards, a delighted Valverde stated: “It was a match where we weren't at our best in the first half. Our intention was to keep the game open for the second half.
"We made the changes in the second half and it worked out well. The victory came, which is a huge joy for the club, the players, and the fans. It leaves us with a chance at San Mamés.
“We try in every match, today we had the effectiveness we lacked on Sunday. Everything is ultimately decided in the penalty areas, that's what we want. We have very important league matches ahead, starting this Saturday, and we want this result to give us a boost.”
While Athletic won't reach the knockout phase, Valverde says they have appreciated the run.
He added, “Our Champions League run has been incredible considering the opponents we've faced. Dortmund overwhelmed us in the first half there, and PSG and Arsenal were superior.
"I consider it extraordinary, unlike the league, which I can't describe as such. I don't think we'll win the Champions League, but we'll try (laughs).”