Valdes, who has spent his entire professional career at the Nou Camp, announced on Thursday that he did not plan to pen a fresh deal when his current contract expires at the end of the 2013/14 season.
Following the "irrevocable" decision not to renew, Zubizarreta made it clear on Friday that the Catalan giants had wanted to keep the player - but claimed discussions did not get that far.
"We have to support him and encourage him as much as we have done throughout his career," Zubizarreta said on www.fcbarcelona.com.
"We were holding the first meeting to initiate the process for renewing Victor's contract. The meeting began with us expressing the club's desire to extend his contract, because we consider him to be a top-class goalkeeper.
"But before we could make any proposal or discuss anything, his agent said the decision was already made and meditated, and that he will not be staying any later than June 30, 2014. It is an irrevocable decision."
Zubizarreta urged Barca's fans not to turn on Valdes, who has been the club's number one throughout the last decade.
"(We must) respect the professional decision of a player who has spent 12 years in this home," he added. "With that in mind, we are asking you to continue supporting him and to encourage him as much as you have done throughout his career.
"He is committed to this jersey until June 30, 2014 and will defend the goal with everything he has and knows.
"Meanwhile, we shall work together to see what the next steps should be, along with him and his agent, to work together to deal with this situation that arose yesterday [Thursday]."
Barca coach Tito Vilanova was surprised by Valdes' decision, but remained full of respect for the player.
"I encouraged him to renew," the 44-year-old said this afternoon. "I had a sense that he would renew, but negotiations never got started. He was direct and we must respect him."
Vilanova, who has spoken with Valdes since the announcement, insisted this on Friday the goalkeeper was not unhappy at the Nou Camp and would remain the club's number one - form permitting - until his departure.
"I have talked with Victor, one on one, and it was a private conversation. We have to respect his decision," he said.
"I've seen him happy and content. I do not think he is unhappy with us.
"I understand some people think it is not a good time to go, but it gives the club time to find a replacement in a very difficult position.
"Anyway, every player is entitled to do what he wants. There is no doubting his professionalism.
"Sometimes we think Barcelona is the best club to play at but we all have the right to play elsewhere, experience other cultures... He's a free man. I respect him a lot."
He added: "I do not know if Victor can change his mind. I believe it is irreversible, but I do not know.
"Victor gave us 18 months to look for another goalkeeper. He's honest. This is not about the money - talks didn't even start."