The Basque club were 3-1 aggregate winners, after reigning 2-0 at Espanyol's Cornella-El Prat in the second leg on Wednesday.
Aggressors from the outset, Bilbao struck twice in the first half via Aritz Aduriz and Xabier Etxeita to put the tie beyond doubt - with Espanyol unable to get even one of the three goals they required thereafter.
Coming into the clash, Espanyol had the slight advantage - as a home 0-0 draw would have sent them through to the final on away goals.
But it was Bilbao who progressed to the May 29 decider, which will see them play Barcelona in the Copa final for a third time in seven years.
"Espanyol played well in the first leg," Valverde told reporters.
"There we had a moment of weakness and it was not [fully] exploited by them.
"Tonight, we didn't give them a chance, though."
Valverde immediately set about playing the underdog card for his side, who have twice lost to Barca in the Copa del Rey decider recently - losing 4-1 in 2009, and 3-0 in '12.
"Barca are the favourites, obviously, but we don't care who we're playing," he said.
"The important thing is that we reached the final. Our opponents have a lot quality and experience, but we have to use our potential and anything can happen."
Espanyol boss Sergio lamented his side's inability to get through to their first Copa final since winning it in 2006.
"We missed an opportunity, but I want to be positive and thank the players for their efforts to bring us here," Gonzalez said, according to Espanyol's website.
"I also want to thank you immensely for the fans as they have been with the team. They have been at the height of the semi-final.
"Athletic has done better in the first half.
"They had an opportunity and we have missed another and have failed ... too bad the second goal has been [scored] so quickly and the magic is lost. We must lift our heads and move on."
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