The Hoops boss recruited a number of players at the start of the year, with the West Bromwich Albion striker holding out for a move by driving down to Loftus Road in hope of securing a transfer.
However, no deal took place between the two sides for the player and Redknapp feels that the Nigerian could have kept QPR in the Premier League.
"I would not have changed an awful lot [this season], really," Redknapp told ESPN. "I'd have probably tried harder to get the boy from West Brom, Odemwingie.
"He might have really given us something up there with Bobby Zamora not being 100 per cent fit. He might have scored four or five goals that make the difference.
"He did no different to what about 50 other footballers did on the same day. He made one big mistake. He was too honest, he turned up at the football club, he was silly."
Rangers sit 10 points adrift of the safety zone and look destined for relegation to the Championship.