The current Queens Park Rangers boss was the clear favourite to take over from Fabio Capello in May 2012, but the Football Association eventually opted for Hodgson without even asking Redknapp to come for an interview.
"Roy Hodgson is a very good manager and a lovely person, but I just think he fitted as someone safe and secure. He wasn't a gamble and that's why I very rarely enjoy watching England," he told talkSPORT. "I do think we'd have qualified for the World Cup by now if Harry Redknapp was in charge, but I'm biased.
"Harry gives players more freedom and flair. Roy always sets his teams out not to lose whereas I think Harry sets his teams out to win. There is a massive difference.
"The thing about Harry is he just goes out to win. It wouldn't have fazed him. I desperately wanted him to take over. I know there were all sorts of things in the cupboard at that time and everybody thought there would be problems."
Redknapp has also criticised the FA and branded them 'clueless'.