Redknapp's move to sign the West Brom striker fell through as the transfer window slammed shut, the Nigerian famously turning up at Loftus Road only to be refused entry after the clubs were unable to agree a deal.
However, Redknapp, whose side are 10 points adrift of safety with only four matches remaining, believes the additional firepower of Odemwingie could have made all the difference.
"I would not have changed an awful lot, really," he said. "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."