Greater Manchester Police received the emergency call at 10.30pm last night just after the final whistle, when United were knocked out of the Capital One Cup by Sunderland, who won 2-1 on penalties after extra time.
In an audio clip released by the force today, the supporter can initially be heard asking to speak to the Red Devils' former boss to discuss the "total and utter rubbish" result.
When told it would not be possible to speak to Sir Alex, he said he was calling 999 to report the crime of his team being "completely knackered".
Sir Alex managed Manchester United from 1986 until he retired in May last year, and was succeeded by David Moyes. During his 26 years at the club, he won 38 trophies, including the European Cup, 13 Premier Leagues and two Uefa Champions League titles.
Greater Manchester Police released a statement on their GMP Manchester North Facebook page which read: "Last night, at approximately 10.30pm 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 your 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 inquiries 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."
Diane Grandidge, GMP's business lead for call handling, said: "Silly calls like this one are thoughtless and can make a difference in a life-and-death situation. As a force we receive thousands of emergency and non-emergency calls, which is why I would urge those considering making such pranks to think twice.
"Our call handlers should be able to focus their efforts on real emergencies as they are happening. Hoax calls could delay an officer responding to a real emergency. You wouldn't want your own emergency call being delayed by someone tying up a line with a hoax."
In an audio file released today, the 999 call handler can be heard asking: "Hello. You are through to the police. How can I help?"
Unidentified caller: "Could I speak to Sir Alex Ferguson please?"
"Not by a 999 line, I'm afraid. No."
"Er... Sir Alex... The result is all wrong. They had extra time and it was a total and utter load of rubbish."
"Sir, you're actually on a 999 police line. Is there a crime you'd need to report to the police this evening?"
"Yeah, a crime. Yeah, I'll report a crime."
"And what crime is that?"
"The crime is that Manchester United, Manchester United were absolutely knackered."
After asking for his name and home address, the call handler added: "OK, I'm going to clear the line now, OK?"
"Yeah, can you phone me back then? You must have my...?"
"No, I can't phone you back because it's not a police matter"
"It is a police matter. Are you a policewoman?"
"No I'm not a policewoman. I'm a member of police staff. This is not a 999 matter."
"A 999 matter. Oh, I see. Right. OK then, umm."
"I'm going to go now. Goodbye."
"Okay, bye, bye."