The striker travelled down to Loftus Road in the hope that he would be granted permission by the Baggies to join Queens Park Rangers.
However, QPR failed to come up with a deal that was deemed suitable by West Brom and a transfer never materialised.
"This evening's developments have brought a conclusion to what has been an unsavoury affair. As our sporting and technical director Richard Garlick has repeatedly said in recent days, we had no need or desire to sell our core players," Peace told the club's official website.
"The only way we would have considered letting Peter leave was if an acceptable offer was forthcoming and if we had found a suitable replacement at relatively short notice. Neither materialised and, in the end, the matter became a point of principle as much as anything.
"Peter has acted wholly unprofessionally. He must now accept the fact he remains under contract for a further 18 months and has to focus on his Albion commitments."
Odemwingie is expected to be at training with his West Brom teammates tomorrow morning.