Moyes succeeded Sir Alex Ferguson last summer on a six-year contract but was sacked before his maiden season was out, with United finishing 22 points behind rivals and champions Manchester City in the Premier League and failing to qualify for Europe.
Vidic's eight-and-a-half-year association with the club ends with a move this summer to Serie A side Inter Milan, and he concedes his final season did not play out as he would have hoped.
"The players were being questioned, the manager was being questioned, the club was being questioned," he told BBC Sport, reflecting on a campaign which saw poor results from the outset.
"People end up saying the players are not good enough and we need to buy better ones.
"I am not saying we have had a good season. It was a bad time and the players could have done better. But everyone lost belief in the team."
Moyes struggled with the step up from Everton to Old Trafford and his tactics were criticised, notably after the 2-2 draw with relegated Fulham when they racked up 81 largely aimless crosses before conceding a stoppage-time equaliser.
Vidic told the Daily Telegraph: "I am not saying that the David Moyes way was bad, but these players feel more comfortable playing a certain way of football.
"You have to respect where you are and what you represent, though, and there is no point speaking about someone who was here, who everyone knows lost his job because he did not succeed in doing what he wanted to achieve.
"The best I can say is that he tried really hard, he was professional. He was really committed to the job and desperately wanted to do well. But unfortunately, it didn't happen and we are all sad."
The Serbia international acknowledges strong words were exchanged within the squad but denies any were aimed at Moyes.
"The players did argue among ourselves," he told BBC Sport. "But we were arguing to get better.
"It hurts but we could say those things to each other because we have been together for so long. We never argued with the manager or his assistants. Never.
"It is not the players' job - not even the captain - to tell the manager he should play this way or that.
"People said we lost faith in David Moyes. We didn't. We knew he was trying to build something.
"The captain has to respect the club. You will never hear from me that (Moyes) did this badly or that badly."
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