Zola told Sky Sports News: "We wanted to keep Bellamy, we tried everything to keep him. He decided he wanted a new experience - simple as that.
"We couldn't hold a player who was so determined to leave."
When asked directly about the strike claims, he replied: "No he didn't go on strike.
"He didn't train one day because he had a problem in his calf and the day after was not a compulsory day, so he didn't train again.
"I don't want to talk about strikes or anything like that. Craig Bellamy has decided to go and that's it, end of story."
Zola also reiterated that the Hammers will not part company with any player who is committed to the club.
He said: "I don't think so, I don't think that is the case (that Bellamy wanted to stay).
"The fans have to be confident when I say that somebody wants to stay here, we don't want to sell players that are important for the team unless they want to go."