Despite being second all-time record winners behind only Barcelona, Los Leones last won the trophy 40 years ago.
The 23-time victors, appearing in their 40th final, are favourites against Mallorca for the clash at La Cartuja stadium in Seville.
“We always have to try to win, but we have played five (Copa) finals this century and we have lost all of them,” Valverde told a news conference Friday.
“When you have nothing, you have nothing to lose.
“We will try to win, not just to thank the fans, but also for us, for our responsibility to the club that we represent.”
Athletic’s only silverware since the domestic league and cup double in 1984 have been two Spanish Super Cup triumphs, in 2015 and 2021, both against Barcelona.
They fell to defeat in the 1985, 2009, 2012, 2015, 2020 and 2021 Copa del Rey finals.
Despite Athletic, fifth in La Liga, being expected to beat underdogs Mallorca, 15th, Valverde said anything could happen.
“I don’t think you can talk about victims and favourites,” said the coach.
“The game is open, they have the same chances as us, you have to fight it out on the pitch.”
Mallorca coach Javier Aguirre said his team could not afford to make a single mistake against Athletic if they wanted to win the cup for the first time since 2003.
“You can’t just do it with hope or with calm, you have to play, and play well, and don’t make mistakes because if you make errors they will condemn you,” Aguirre told a news conference.
“We have to have almost the perfect game — hope is not enough, it helps you, but you have to have a good game.”
Aguirre, who took Osasuna to the 2005 Copa del Rey final but fell to defeat against Real Betis, said he would go to a monastery on Mallorca if his team won.
“I promise that if we’re champions, I’ll go to Lluc,” said the veteran Mexican coach.
Aguirre, born in the Central American country to two Basque parents, said his family would be supporting Athletic.
“I made them doubt it, but they’re with Athletic,” he said. “In my house, everyone was Athletic, me included.”
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