A move for the 31-year-old collapsed in bizarre circumstances after Odemwingie wrote a series of critical remarks on Twitter and attempted to force a deadline-day move to Loftus Road by driving to London in January.
The Baggies refused to sanction the transfer and the striker was subsquently reportedly fined two weeks’ wages totalling £75,000 - and Redknapp believes Odemwingie could have added more bite to the Rs attack.
|9/2||Reading and QPR are 9/2 with BetVictor to be drawing at half-time and full-time on Sunday
"He might have really given us something up front, with Bobby Zamora not being 100 per cent fit. He might have scored four or five goals that make the difference.
"We couldn’t have got much closer to signing him - he was outside our front door - but he made one big mistake, the kid. He turned up at the football club, he was silly. But he did no different to what about 50 other footballers did on the same day."
A 2-0 loss at home to fellow strugglers Stoke City leaves QPR on the verge of relegation, with a win for Aston Villa over Manchester United on Monday night enough to send both the Rs and Reading down.
And Redknapp appears consigned to spening next season in the Championship but, either way, he hopes to be able to refresh the squad ahead of the 2013-14 campaign.
He continued: "I’d rather have the challenge of building another Premier League team here, which I would have done, and that we weren’t in trouble. But this is where we are - I’ve tried my best with what we’ve had and it’s not been good enough.
"Not that long ago I was managing in the Champions League with Tottenham but that’s life. The San Siro was great - I loved it, fantastic. It was great going to Milan and winning, but this is where I am now and I will get on with the job.
"The thing that makes me laugh more than anything is when I hear people saying, ‘They have gone down, they won’t want to play in the Championship’. Well, who put them in the Championship in the first place? Let’s get one thing straight, they are in the Championship because they weren’t good enough in the Premier League.
"Do they owe the club to stay and get QPR back up? Well, that depends on who you want to keep. You’d like to freshen it up if you could. I’d like to go out and build my own team in the summer if I had the chance but I don’t know whether I’ll be able to."