Ferguson bows out next Sunday after securing a 2-1 win over Swansea in his final home game as manager.
After the victory, he addressed the crowd and told them to get behind his replacement.
"I would like to remind you this club stood by me in bad times, the players and the staff," he said.
"Your job now is to stand by the new manager."
Ferguson paid personal tribute to Paul Scholes, who started the game and will also retire in the summer, and Darren Fletcher, who continues his recovery from a chronic bowel condition.
And he insisted he would still be a regular presence at Old Trafford.
"I will be able to go along and watch them rather than suffer with them," he said.
"Those last minute goals, the comebacks and even the defeats are part of this great football club. It has been an unbelievable experience."