The Scot thanked his family and made mention of his 11 grandchildren, all of whom were in attendance.
He left the field before returning with his players to raise the trophy and take part in prolonged celebrations on the pitch.
Ferguson walked back down the tunnel for the final time as manager and then gave a series of media interviews.
"Fantastic, what a send-off," he said.
"I was bubbling there for a bit. All those flags, the atmosphere today was unbelievable the whole game. I'm proud of my fans today."
He confirmed that striker Wayne Rooney, who was not involved in the Swansea match, has handed in a transfer request.
Ferguson says emotional farewell
"We have refused it,"
Ferguson told BBC Sport.
"He should go away and think it over again. He wasn't happy about being taken off a few times this season - but a Wayne Rooney in top form wouldn't be taken off."
Ferguson revealed when his decision to retire was taken and a key reason behind it.
"I decided to retire last Christmas," said the former St Mirren, Aberdeen and Scotland boss. "Things changed when my wife Cathy's sister died. She has lost her best friend, her sister. Also, I wanted to go out a winner.
"It was very difficult [not to reveal it]. There were times when we sometimes blurted it out to the family. We told our sons in March. My brother didn't even know until Tuesday.
"I've got a lot of things to do. My son, Jason, has been organising things. I won't be sitting still."
Ferguson added that his most important achievement was the first league title with United in 1993. "The door opened after that," he said. "We just grew and grew and grew. We had some fantastic teams."
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