The 20-year-old was sent off for a challenge on centre-back Jonny Evans in the first half, and was furious with the role he believes Sir Alex Ferguson played in the dismissal.
"I apologise to the fans for getting sent off but no way was I pulling out of that tackle in a game of that importance. Im sorry," Shelvey posted on Twitter.
"I have also apologised to sir Alex, just where I come from people don't grass people up to get someone sent off."
|Shelvey red with rage at 'grass' Sir Alex