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"It was a bad time and the players could have done better. But everyone lost belief in the team," Vidic, who has agreed to join Inter Milan, told BBC Sport.
"People said we lost faith in David Moyes. We didn't. We knew he was trying to build something."
Moyes endured a disastrous campaign after succeeding Alex Ferguson as manager last year and was sacked in April, with United going on to finish in seventh place in the Premier League and failing to qualify for Europe.
While Vidic, who spent eight-and-a-half years at United, conceded that the players had argued about how to turn the club's fortunes around, he insists that Moyes was never the target of their anger.
"The players did argue among ourselves. But we were arguing to get better," he added. "We never argued with the manager or his assistants. Never."
Player-coach Ryan Giggs succeeded Moyes on an interim basis and United are reportedly close to appointing experienced Netherlands coach Louis van Gaal as their next permanent manager.
With Vidic's long-term partner Rio Ferdinand also leaving the club, United find themselves in need of a new first-choice centre-back pairing.
England internationals Phil Jones and Chris Smalling will now hope to establish themselves at the heart of the United defence, but former club captain Roy Keane has been critical of their progress.
"We were told two or three years ago Jones was going to be the new Duncan Edwards and Smalling was this and that," Keane said, in comments reported by several British newspapers on Wednesday.
"I've watched United live nine or 10 times this year and they have been none of those things. If anything, I think they have gone backwards.
"Jones needs to toughen up. He's playing for Man United. Every time I see him he is getting carried off."
