The 31-year-old striker had been a target of QPR throughout January and, when he drove to London and addressed a media scrum talking about a move to Rangers, it appeared a deal was on the table. But Albion quickly released a statement saying Odemwingie was there without permission and QPR said they had stopped him from getting into their Loftus Road ground.
Writing in The Sun, Redknapp stuck up for the striker, saying: "There have been countless players guilty of doing things a million times worse than Peter Odemwingie. But from the stick he's got over the past 48 hours, you would never believe it. And I really, genuinely hope that all those people having a pop at him now give the lad a break because, if he's guilty of anything, it's being too honest."
Redknapp, who suggested a proposed loan deal of a player from QPR to West Brom was the reason for the move breaking down, explained the day's events from his perspective.
"It looked as though the deal was going to happen," he said. "We had got a price off West Brom, the kid himself thought it was all on and obviously so did his advisors. So it wasn't out of order for him to jump in his car and head to London.
"Peter just wanted to make sure he was in the London area so the deal could go through before that deadline.
"It would have looked even worse if it had fallen through because he hadn't got here in time."
He added: "The one thing I think Peter did wrong in all this was to actually drive to the ground. If he'd parked down the road, no one would have been any the wiser and - as disappointing as it would still have been for all sides - no harm done."