The English FA will wait for referee Mark Halsey's report to arrive today, but it is expected that the official will confirm that he missed the incidents and the governing body will launch retrospective action.
Fellaini, who was captured on video headbutting Shawcross at a corner, before elbowing him and slapping him in the head in two separate incidents, is unlikely to be given a lengthier ban.
Although the butt was an unsightly incident, the FA would only mete out a longer punishment if it considered an offence to be exceptional, which is unlikely in this case. Had Halsey seen the offence, Fellaini would have received a red card and a three-game ban, which is why the FA is set to hand out that standard sentence.
The Everton midfielder's indiscretion, which is also expected to lead to him being fined two weeks' wages, around £120,000, came early in the second half while he had been jostling with Shawcross during a corner shortly after Stoke's equaliser.
Angry Stoke players have called for the FA to take stern action, with goalkeeper Asmir Begovic saying: "I was a little bit unhappy with what was going on with me and the holding and the shirt-pulling and everything else that wasn't being dealt with.
"I made my point clear and probably deserved a booking. I should have gone about it in a better manner but, in the heat of the game, sometimes that happens."
Stoke manager Tony Pulis believes this is the third time in recent weeks that referees have not acted on bad fouls against his team, referring to incidents involving Chelsea's David Luiz and Aston Villa's Ciaran Clark.
A statement, in which Fellaini apologised, was later released. He said: "I apologise completely to Ryan Shawcross, my team-mates and to our fans at the game. I lost my temper and it was unprofessional.
"There was a lot of pushing and pulling going on inside the penalty area and I didn't feel I was getting any protection from the officials. Nevertheless I know I shouldn't have done what I did. I have also apologised to the manager and the staff – I have no excuses."
Everton's hopes of remaining in the top four will not be helped by the absence of the influential Fellaini and Moyes called the midfielder's behaviour "unacceptable".
Their midfield will be weakened by Fellaini's ban, but their lack of numbers in attack remains a more pressing concern with reinforcements expected next month.
Everton scored against Stoke through a Shawcross own-goal, but he made amends by launching a long ball that led to Kenwyne Jones heading in their equaliser. (© Daily Telegraph, London)