Odemwingie has had a strained relationship with the club ever since January, when the forward tried to force through a move to QPR.
At the awards ceremony last night, the ITV Sport presenter said: "Our fourth award of the evening is Tweet of the Year. Oh, no, sorry, it's Twat of the Year and the winner is Peter Odemwingie."
However, Chiles's comments have drawn criticism from Albion manager Steve Clarke.
"It was a ridiculous comment to make," Clarke told the Daily Mail.
"I didn't like it. I didn't say anything about it at the time, but I'm saying it now — it was a stupid comment. It was out of place. It was a West Bromwich Albion awards night. There was no place for it.
"Peter had permission from me not to go to the event. Peter's one of my players — I protect my players fiercely."
Adrian Chiles, who used to present Match of the Day 2, is a lifelong Baggies fan, along with fellow celebrities Frank Skinner and Lenny Henry.