Al Fayed has reacted after his side was denied a penalty at Old Trafford two weeks ago when Manchester United midfielder Michael Carrick appeared to bring down Danny Murphy inside the area.
As a result, Al Fayed has urged the two governing bodies to "wake up" and make improvements.
"The FA's problem in addressing this pivotal situation is that it has too much power. Where else can decision makers escape all responsibility to admit serious and blatant errors and have the protesters fined on charges of misconduct?" read a statement from Al Fayed on the club's official website.
"The losses that we incur from such careless decisions have a huge impact and can have calamitous consequences. Referees are all too easily influenced by the more powerful clubs and individual owners which calls into question the integrity of both them, and the governing body that they report to.
"It is time for the Premier League to wake up. They have been in a coma for a long time. Lots of clubs are suffering from such stupid decisions. Advanced technology is available and it is evidently being used in other sports."
The Premier League and FA have yet to provide a reaction to Al Fayed's statement.