The BBC's Dan Roan interviewed City's Football Development Executive Vieira at the Soccerex Forum in Manchester, and reported the former Arsenal midfielder's claims that cross-town rivals Manchester United and other major teams get the benefit of refereeing decisions when they play at home.
The club have backed the Frenchman, and banned Roan from "all Manchester City media activity".
"When United play at home they get some advantages that other teams don't get," Vieira was reported as saying by the BBC.
"When you go to United, Madrid, Barcelona, or Milan, it's always difficult for the referee to go against these kind of teams.
"This is the way it is. It's something the teams who are used to winning get all the time, so we need to win games so we have this advantage in the future."
The comments were taken as a barb in the wake of Michael Oliver's refusal to give Fulham a last-minute penalty at Old Trafford on Monday evening that could have denied United two crucial points in the Barclays Premier League title race.
But in a statement on the Manchester City website, Vieira voiced his anger at the way the story had been reported without context.
“I am very angry with Dan Roan," Vieira said. "I feel he has misrepresented me. I made it clear in the interview twice that I wanted to avoid criticising United and even stated that I didn’t watch the United game against Fulham and had not seen the incident to which the reporter referred.
“That part of the interview was ignored and my comments were taken completely out of context. I called the reporter twice to ask for a retraction and an apology which has not come. I feel Dan Roan and the BBC have shown a complete lack of respect for me, the ‘Football Against Hunger’ charity and Manchester City Football Club.”