Valencia beat Barcelona 2-1 to win the Copa del Rey on Saturday, ending the Spanish champions' four-year winning streak in the competition and denying them a domestic double.
Kevin Gameiro and Rodrigo Moreno struck first-half goals to give Marcelino's dominant Valencia control of the final in Seville's sweltering Benito Villamarin stadium.
Goncalo Guedes missed a gilt-edged chance in stoppage time for Valencia, but they held on to win their first major trophy since last lifting the Cup in 2008.
"I'm so happy because for me, my family, it's incredible," Valencia captain Dani Parejo said. "A club like Valencia deserves a lot more joy like this. I don't have the words, it's incredible.
"We've made history in a really significant year, our centenary year."
Valencia finished fourth in La Liga after a strong second half of the season, reaching the Europa League semifinals and ending an impressive campaign with this victory.
By contrast, Barcelona's campaign collapsed in the past fortnight as they threw away a three-goal Champions League semifinal lead to be eliminated by Liverpool before letting the Cup slip out of their hands.
Barcelona were bidding to lift themselves from their humiliation on Merseyside by securing the ninth domestic double in their history, but despite Messi's efforts, they were overrun by a determined and well-drilled Valencia side.
The Catalans failed to create openings, and Rodrigo nodded home the second after Carlos Soler whipped a ball across the face of goal.
Messi struck the post with a delightful outside-of-the-boot effort before slotting home the rebound for his 51st goal of the season when Jaume Domenech saved Clement Lenglet's header, but it was not enough.
"Valencia are worthy champions, and it's also been a good year for us," Pique said.
"It's always a good year when you win La Liga, but the expectation was to have an even better year, and that's not been the case. The season ends with a bittersweet feeling, because it could have been better.
"We aren't worrying about the manager's future, we must analyse ourselves and try to improve. The other decisions aren't in our hands, but we've said more than once that we would like him to stay on."