Peace said: "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.
"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.
Odemwingie made a mistake - Redknapp
"Neither materialised and, in the end, the matter became a point of principle as much as anything."
Peace added: "He must now accept the fact he remains under contract for a further 18 months and has to focus on his Albion commitments."
Odemwingie had appeared optimistic that a deal could be reached when he was interviewed on his arrival in west London.
"I hope they will be happy with what they get and, of course, they want to get in players themselves. I just hope that everything will be sorted out in the next few hours," Odemwingie told Sky Sports News at the time.
The Nigeria international had previously been quoted as saying that he had reached an informal agreement with West Brom on his departure, only to find that the situation had changed when he was en route to London.
"I am disappointed this is all happening. I met with [Albion sporting and technical director] Dan Ashworth this morning and we shook hands that I could leave with his blessing if the £3.5m fee was met," the striker told
the Daily Mirror.
Odemwingie's Premier League prowess
The former Lille striker has scored 30 times in 80 Premier League appearances, including a hat-trick against Albion's rivals Wolves
Redknapp said earlier in the day that Odemwingie was still a player he would like to bring into his squad.
"He's got pace, I really like him and I think he could help us," he told the the club's official weekly phone-in show 'London Call-In'.
But West Brom's determination to retain the player appears to have won out.
Odemwingie, a £2.5m signing from Lokomotiv Moscow in 2010, tweeted on Sunday night: "Looked through my tweets. Deleted some. Was too much. Only excuses - home alone, dark, son and wife in hospital, frustrated."
His deleted tweets included: "Last season January window is when I should have handed in transfer request. Was one foot in Rubin Kazan - not for sale. Fulham. Not for sale. Newcastle. Not for sale. Wigan. Not for sale."
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