The official has asked his superiors at his governing body, the PGMOL, to pass on his regret at awarding Manchester United a spot-kick when Cristiano Ronaldo was clearly tackled fairly by Jlloyd Samuel on Saturday.
It is the second time in just over a year that Styles has had to apologise for a penalty error after pointing to the spot at Anfield in August last season when Liverpool full back Steve Finnan collided with Chelsea's Florent Malouda.
The Daily Mail says the referee realised his mistake almost immediately from the reaction of everyone around him and subsequently confirmed it was an error when reviewing the game on video.
He wanted to apologise publicly after the match and was frustrated that he could not without breaking guidelines from the PGMOL.
Instead, it is thought he sent a separate email with his match report to his manager at the body, Keren Barratt, yesterday asking them to say sorry for him.