In an interview on the BBC's website filmed at the Soccerex conference in Manchester where Vieira was representing charity Football Against Hunger, he said: "When United play at home they get some advantage that other teams don't get.
"I think when you go to United, Madrid, Barcelona, or Milan, when the referees referee these kind of games, it's always difficult to go against these kind of teams.
"This is the way it is."
Vieira, who enjoyed many title battles against United while at Arsenal, was speaking two days after Fulham had a strong penalty claim turned down near the end of their 1-0 defeat by the champions at Old Trafford.
Victory allowed United to go three points clear of City, with whom Vieira is now a football development executive.
City responded to the BBC's claims, saying Vieira had been misrepresented and that the reporter concerned had been banned from any media activity at the club.
"Patrick Vieira has expressed his disappointment and anger at what he feels is a serious and cynical misrepresentation of an interview he gave to the BBC," City said.
Vieira said he had wanted to avoid criticising United.
"I didn't watch the United game against Fulham and had not seen the incident to which the reporter referred," he said.
"That part of the interview was ignored and my comments were taken completely out of context."
The incident came less than a week after Vieira provoked United manager Alex Ferguson by saying they had shown weakness in bringing Paul Scholes out of retirement.
Fergsuon responded by labelling City "desperate" recalling outcast Carlos Tevez after the Argentine's much-publicised falling out with manager Roberto Mancini following his refusal to warm up as substitute in the Champions League against Bayern Munich in September.
Vieira, who made 28 appearances for City after joining from Inter Milan, said that despite his club seeing their lead disappear in recent weeks, they deserve to win their first English title since 1968.
"Since the start of the season we've been the best team and played the best football," Vieira said.
"I believe the club deserves it. When you are first you have the advantage, (United) are favourites."
He also returned to the subject of Tevez.
"We're glad Carlos is back. The quality of these kind of players will be really important at this stage of the season," he said. "The issue was between him and the club. The players were really pleased to see him back."