Redknapp said a fee of £3.5 million plus the loan of Junior Hoilett had been approved with his blessing but things started to fall apart when Hoilett told QPR he did not want to go.
Clarke claimed Odemwingie still had a future at his club but would have to consider apologising first.
"He has to get picked, he has to get back into the squad, he has to show his team-mates he is willing to help them and, if he is selected for matches, he has to do well in the games.
"I can't say for sure he hasn't played his last game for the club but I don't think he has played his last game for the club. I don't have a big squad and hopefully we can get to a situation some time in the future where if we need to use Peter, we can."
Redknapp, whose side took on Norwich City overnight, denied QPR had encouraged Odemwingie to come to London on transfer deadline day.
"He didn't set foot inside the ground. He just pulled up in his car, as you saw on TV," Redknapp said. "He definitely wasn't in the building. He stayed outside but he made a mistake by coming down here. He shouldn't even have done that.
"I think he wanted to be around just in case the deal got done and he was on hand for the paperwork and a medical. He's probably driven down to London and thought, 'Where do I go now?' and he's headed for the ground.
"We played it by the book and West Brom have been fine about it. They are happy with the way we've dealt with it. The boy's just made a mistake. If you don't pitch up outside the ground, there's no problem, is there?
"It's a shame because he's a nice person, a good guy. I met him two years ago and he's a very educated boy, and he's not the first one who has found himself in a situation where things haven't worked out the way he wanted. He'll probably get some stick now but a lot of people in football get stick, don't they?"
Redknapp admitted he had tried to sign a third player from Spurs, David Bentley, but that the former England international's wages were a bit heavier than the others.
He said he had got good value on the deals for Tottenham's Andros Townsend, on loan, and Jermaine Jenas, who has an 18-month contract.
"I think you'll find the wages only come to around £25,000 a week," he said.
Aside from Chris Samba, a £12.5 million signing, Redknapp denied QPR had spent disproportionately big on Premier League survival relative to other clubs in the past.
"The chairman [Tony Fernandes] said to me a couple of weeks ago, 'If you had the choice for a centre half to replace Ryan Nelsen, who would you go for?' So, I said Rio Ferdinand, [Nemanja] Vidic, John Terry, Chris Samba.
"The chairman did the deal. It wasn't a case of me saying, 'we've got to get Chris Samba in here'. It was the chairman, with the other shareholders, completely off his own bat."
Redknapp said QPR's former England fullback Luke Young is close to retirement having failed to return from operations on a long-standing injury affecting his ribs and hips. Young, 33, won seven caps but has not played since March.
"I think his future has got to be in doubt," Redknapp said.The Independent
