Valencia denied La Liga champions Barcelona the chance of a domestic double in the final of the Copa del Rey in Sevilla on Saturday.
Barcelona midfielder Ivan Rakitic admitted that the loss "hurt" and his side would need to be "self-critical" in the off-season after suffering damaging defeats to both Valencia and Liverpool in the Champions League semi-finals.
Valencia's captain Dani Parejo was "speechless" after winning his first trophy at Valencia since joining the club eight years ago.
Kevin Gameiro and Rodrigo scored two first half goals and despite Lionel Messi's 73rd-minute strike, Barca fell short.
After the match, Barcelona president Josep Maria Bartomeu backed Valverde to continue at the Nou Camp.
This was Valencia's first piece of silverware for 11 years, when they last won the Copa del Rey.
Victory also meant coach Marcelino Garcia Toral ended a personal 20-game winless run in all competitions against Barcelona.