Having lifted the trophy in four consecutive seasons, Barca were undone by first-half goals from Kevin Gameiro and Rodrigo in Seville, and couldn’t find a way back into the tie despite Lionel Messi’s 73rd-minute strike.
Valencia held on to win their first major trophy since last lifting the Copa del Rey back in 2008.
The defeat denied Barca a domestic double after they picked up the La Liga title following a solid campaign that saw them lose just three of their 38 games and finish 11 points clear of runners-up Atletico Madrid and 19 ahead of bitter rivals Real Madrid.
However, Pique conceded that despite their league triumph, the season as a whole – which included their infamous collapse against Liverpool in the Champions League semi-final – has left a “bittersweet” taste in the mouths of the Barcelona players
“As long as the La Liga title is won, I always say it's a good season,” he said to Teledeporte, “but the expectations were for a much better year.
“It was not like that, and we leave with the bittersweet taste because we could have been better.
“They (Valencia) arrived twice and scored two goals in the first half. I am proud with the reaction of the team - we have made a great goal and almost got a draw, but we have to congratulate Valencia. They are well-deserved champions.”
The result was not so gracefully received by a large number of Barca fans – many of whom took to social media to voice their displeasure at manager Ernesto Valverde.
But Pique was quick to defend the 55-year-old, and insisted the players are keen to see the Spaniard stay at the Camp Nou after he delivered the club’s fourth La Liga title in five years.
“In the end, there are decisions that are not in our hands,” he said. “This is something that we cannot control. But we would like him to continue, as we have already said. He did very well.
“We do not worry. We have to make an individual analysis and of what we can improve.”
When asked if Barca had missed the influence and guile of Luis Suarez, who was absent from the starting XI after undergoing recent knee surgery, Pique added: “If you do not win, and you have absences, you can always blame it on missing players, but there are no excuses.
“We are Barcelona and we are obliged to win everything, especially this final against Valencia. Next season we have to fight again, for all of the titles.”