Fellaini clashed with centre-back Ryan Shawcross at three separate corners in the Stoke penalty area. All three incidents were missed by referee Mark Halsey during a tetchy 1-1 draw at the Britannia Stadium.
"I apologise completely to Ryan Shawcross, my team-mates and to our fans at the game," said Fellaini.
"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 apologised 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."