In his 14th Vuelta, Valverde was reportedly due to be a support rider for Giro D'Italia winner Richard Carapaz.
However the 26-year-old's injury withdrawal in week leading up to the race pushed Valverde and team-mate Nairo Quintana into leaders' roles.
"I hoped to get a stage win," the Movistar man said. "But I thought second was impossible."
His second place position was threatened by Tadej Pogacar (UAE Team Emirates) on stage 20 to Plataforma de Gredos. And although the Slovenian took third place off Quintana on the podium, he could not oust Valverde.
"I didn't have any time references when he [Pogacar] attacked," the Spaniard added.
"I changed the setting on my radio by mistake and ended up asking Ion Izagirre (Astana Pro Team) what the gaps were.
"Fortunately some roadside fans started shouting at me that he [Pogacar] had a two-minute gap and I'd need to put my foot down.
"So I did that all the way to the top on the final climb."