Fellaini apologizes for headbutt
Fellaini lunged at Shawcross as they jostled at a second half corner but it wasn't seen by match officials. The Belgium international could find himself in trouble when Football Association disciplinary chiefs look at the incident on Monday.
"I apologize completely to Ryan Shawcross, my teammates and to our fans at the game. I lost my temper and it was unprofessional," said Fellaini.
Fellaini added: "There was a lot of pushing and pulling going on inside the Stoke 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 apologized to the manager and the staff - I have no excuses. I was disappointed with the way I was being treated and I lost my temper, which was unprofessional of me."
Everton manager David Moyes expressed his frustration following the match, branding the foul as "not acceptable."
''I have told him in the dressing room that it is not acceptable - I won't accept it as a manager that he does that,'' said Moyes . ''It should have been a sending-off."
Everton would have gone level on points with third-place Chelsea had it maintained the lead given to the visitors by Shawcross' own goal in the 36th minute.
Kenwyne Jones equalized with a header in the 50th for his first goal in 28 league appearances, preserving Stoke's unbeaten record at home this season.
The Associated Press contributed to this report.