Qualification from UEFA Champions League Group H was impossible for both clubs before their meeting at San Mames on Wednesday, but Athletic needed just a draw to extend their continental campaign into Europe's second-tier competition.
BATE required all three points, but despite frustrating their hosts for 47 minutes were eventually undone by goals from Mikel San Jose and Markel Susaeta.
Valverde was pleased with the result and revealed part of his side's motivation was to begin to wash away the memory of Saturday's home defeat against Cordoba in La Liga.
"Our goal was to win for many reasons, to be seeded, to win in San Mames, to take away the bad taste of another day in the [Spanish] league," Valverde told the club's official website.
"We thought they would not come here to attack.
"We are in the Europa League and we want to get as far as possible."
Valverde went on to reveal why he did not select regulars Iker Muniain and Aritz Aduriz.
"Muniain was okay, it was a technical decision," said Valverde.
"Markel [Susaeta] and Ibai Gomez are important players for us, they can give us many things.
"Aduriz was not 100 per cent, Guillermo [Hernandez] has also been pretty good, he has just lacked goals."
