Vidic conceded both teams got what they deserved.
"I have to say yes, [it was a fair result]," he told Sky Sports. "In terms of the football, we saw two teams who defended as units. I think a draw was the right result.
"We definitely came here to win the game," he said, "but City are a good team. They are strong and we didn't have too many chances.
"There's big pressure on City to win and this is always a hard place for us to come. At certain times I thought we played some good football, but we didn't create too many chances."