Riether became first player to be retrospectively charged by an FA panel for his challenge on Januzaj towards the end of United's 3-1 win at Craven Cottage.
The German defender stamped on Januzaj's ankle in the last minute of the game, although the incident was not seen by referee Lee Probert or his assistants.
But Riether will now serve a three-match ban after accepting a charge of violent conduct, and he has apologised to Januzaj via his Twitter account.
He wrote: "I want to say I am sorry to Adnan Januzai. It was very unlike me and I can only say that frustration got the better of me.
"I also want to apologise to my team-mates, fans and everyone at the Club, for the ban incurred following Saturday's match.
"I will accept the consequences of my actions, and hope to put it behind me when I return.
"I want the fans to know that I will be working hard to stay fit and will be ready to continue fighting for the Club as soon as I am able.SR"
In a pilot project, an FA panel of three former referees - Steve Dunn, Eddie Wolstenholme and Alan Wiley - will make a ruling on what they believe the official would have done had he seen it.
For an FA charge to follow, all three panel members must agree it is a sending-off offence. In the instance of Riether, the panel were of the unanimous decision that it was an act of violent conduct.
United boss David Moyes, speaking just before the FA confirmed the charge, said: "I hadn't seen it until after the game. It's a bad stamp and it does look deliberate but that's for the referee to sort of deal with on the day...or they look at it differently. It's over now.
"But I do think Adnan needs a little bit of protection or we are going to find he's getting kicked up and down. I do think he deserves a little more than he's getting at this present time.
"He gets kicked up and down in training every day and he gets on with it. He's learnt from the good professionals to get on with it and accept it. He only needs to look at Lionel Messi. He's the best at getting up. We hope Adnan, and I'm not comparing him to Messi - we hope he can react like Messi - but he does need protection.
"It's not a case of asking for protection. It's up to the referees to do what's right. But we will never ask for it."