Tudor was axed as Juve coach in Monday after defeat to Lazio and has since been replaced by Luciano Spalletti.
Zebina told Tuttosport: "Juventus is a club with extremely high expectations. Igor knows the Bianconeri DNA well: you have to win at all costs. So I don't think he was surprised by the club's decision.
"Sending him away wasn't a personal issue."
Meanwhile, Zebina also discussed being relegated with Juve due to the Calciopoli scandal and having two Scudetti revoked.
He added, "We will never stop talking about it. The truth is that we had an exceptional team and we won what we had to win. Unfortunately, that's how it went, but those trophies are mine.
"We're talking about one of the strongest Juve teams in history: there were World and European champions, Ballon d'Or winners..."