Greater Manchester Police (GMP) were called at 22:30 GMT by a man from Crumpsall after the team lost to Sunderland in the Capital One Cup.
GMP said it “can be sad and depressing” when a football team loses a game but asked the public to “remember that 999 is to be used for emergencies only”.
The force suggested contacting the club to speak to the former manager.
Manchester United lost 2-1 on penalties in the semi-final of the competition at Old Trafford under new manager David Moyes.
On GMP North Manchester’s Facebook page, the force said: “A man from the Crumpsall area of North Manchester rang 999 in a drunken state demanding to speak to Sir Alex Ferguson about last night’s result.
“Obviously, it can be a sad and depressing moment when you’re football team loses a game, however, can we all please remember that 999 is to be used for emergencies only.
“For any other police-related enquiries that are not an emergency, you can ring 101.”
“If you would like to speak to Sir Alex about recent football results we here at GMP Manchester North can only suggest you try ringing Manchester United FC directly as you will probably (not definitely) have a much better chance of getting through to him there rather than ringing the police,” the statement added.