Clarke insists Odemwingie will remain in his first-team plans - despite overwhelming jeers when the player came on as a substitute at West Ham.
He said: "Peter has been part of my squad since the start of the season.
"The episode in January was obviously difficult for all concerned but we left the door open, we got him back in the squad and he still has to be part of the squad.
"I run with a small squad and I thought his introduction on Saturday was positive. He had one good run, a fantastic run by James Collins that probably saved a certain goal.
"Our players' dressing room is really good. It's a strong dressing room. We can handle this situation. It seems to be a bigger issue for the media than for us inside the club, certainly inside the dressing room."