The Reds midfielder was sent off for a foul on Jonny Evans shortly before half-time in a highly-charged encounter at Anfield.
Shelvey, 20, aimed a verbal tirade at the United manager as he headed for the tunnel, feeling that Ferguson had influenced the decision by referee Mark Halsey.
However Shelvey, now serving a three-match ban, has revealed that he sought out the United boss after the end of the game to offer an apology.
"I'm a young boy and I was frustrated because it was a big game," said Shelvey. "You come from a council house and before you know it you're playing Man United.
"Emotions probably got the better of me. I was a bit of a silly boy, for having a word with him like that. But I pulled him afterwards and apologised.
"Thankfully, he recognised that it took a man to apologise and hopefully there are no hard feelings there."