A 2-1 defeat at Real Betis' Benito Villamarin in Seville left Barca feeling as though the 2018-19 season has been something of an underachievement despite retaining their LaLiga crown.
But they were humiliatingly beaten 4-0 by Liverpool in the return leg and Saturday's loss robbed them of a domestic double, with Kevin Gameiro and Rodrigo Moreno putting the game beyond Barca despite Lionel Messi pulling one back.
Valverde's suitability has been called into question by many supporters since the humbling Liverpool loss, but Bartomeu backed the head coach.
Speaking to reporters after the game, Bartomeu said: "We have always said that Ernesto has a contract for next season.
"I do not think he's the culprit. We had many opportunities, but they did not find the net. But count the goals and Valencia scored one more than us.
"It is not a season of excellence, but [nor is it one] of failure. We have reached the final of the Copa, the semi-finals of Champions League.
"In the end, we lost two games, but we are out of the Champions League and we are Copa runners-up."
Speaking after the game, Valverde underlined that he was happy to keep fighting at Camp Nou.
"Coaches are always willing to turn things around," he told reporters.
"If I were given the choice between falling in the final or in the quarters or last 16 I prefer in the final. It's hard to face a elimination, I feel good even though we all want to win.
"I'm fine, what we the coaches want when you lose is to have another chance, we want to get up the next day, I know losing is hard and the coach has responsibility."