United were outclassed and out-fought during the loss at the Etihad , as David Silva opened the scoring after just 12 minutes with a composed close-range finish.
Sergio Aguero then doubled the scoreline two minutes after half-time, playing a neat one-two with Riyad Mahrez on the edge of the box before firing the ball past David De Gea in the United net.
Anthony Martial halved the deficit ten minutes later from the penalty spot after substitute Romelu Lukaku was taken down by Ederson, but City made sure of the points late on as Ilkay Gundogan finished off a brilliant 44-pass move.
Vidic, who played for United between 2006 and 2014, and retired from playing nearly three years ago, revealed that he would love to succeed Mourinho in the hot seat.
"To be honest, in the future I would like to be the manager," the Serbian told beIN Sports . "I would like to think that I know things. For me to criticise Jose Mourinho, as someone who may be in the future can become the manager, is not fair."
The Portuguese boss has come under intense scrutiny in the early months of this campaign as his side have fallen way off the pace in the title race while playing a negative brand of football, but Vidic insists that the club knew what they were getting into by appointing him back in 2016.
"It's not the Manchester we are used to watching," he continued. "It's Mourinho's Manchester and, when he came to Manchester, you have to accept that he is the manager who is going to play this kind of football.
"At the end of the day, that's Mourinho's football.”