The former United and England full-back said that with results only slowly improving on the pitch, the club is not being run correctly by those at the top.
"It is a very dire situation at Manchester United," he told Tribalfootball.com in an exclusive interview.
"They are used to top quality steak but they are having roast beef."
Parker singled out Woodward as a key reason behind United's recent struggles in the Premier League, with the club finishing in sixth position last season and sitting in fifth this term.
Woodward became executive vice-chairman of the club in 2013 when David Gill stepped down, the same year Sir Alex Ferguson retired, and has seen the club fail to compete for the Premier League title since, with the Europa League and two domestic trophies their only return.
"It will only get better when things change at the top and things cannot carry on as they are," Parker argued.
"To get top players to the club, they need to have something they can believe in and a project, but at this moment and time there is only one person with a project and that is Ed Woodward. His project is to have a say in everything that goes in and goes out, without having any great knowledge of football.
"As far as I am concerned Woodward should leave the decision making to people that know what they are doing. Manchester United need to be managed, not coached, they need someone to manage the club, manage the team."
Parker played right-back for England during the 1990 World Cup in Italy, where England reached the semi-final, only to be knocked out by the eventual winners Germany.
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