City assistant boss David Platt was left to face the media.
David Platt: "He is a bit angry, as you can imagine.
"He is just taking stock of the situation and calming down.
"He doesn't want to come out here and say anything that might get him in trouble."
"He is angry about everything in general, our performance - we weren't really at it throughout the game.
"We got outworked by Everton. When you do have moments when you can get back into it, it doesn't go for you.
"You know they are going to make you work. If you look at the stats - we have probably covered the same amount of distance, shown the same intensity."
City could have had a penalty when a Carlos Tevez shot struck Fellaini's hand inside the box.
David Platt: "I didn't see whether it brushed Osman's hand but I don't think that would have been given because it has not stopped the flight of the ball.
"I think it has been given for the Fellaini handball. Is it intentional? No, but having given it, it is two or three yards inside the box.
"It is a decision that has gone against us.
"We have an obligation to win football matches between now and the end of the season, regardless of whether there is a points advantage or it is mathematically impossible, which it isn't at this moment."