The 65-year-old boss believes his chance to manage the Three Lions has now gone but claims he is "not bothered" because he has a great job at Tottenham
The Spurs boss was the hot favourite to replace Fabio Capello after his departure from the national set-up in February, but was left disappointed after the Football Association appointed Hodgson earlier this week.
And Redknapp believes that this signals the end of his chance to ever manage England, but expressed his happiness with his current position at the north London club.
Redknapp told BBC Sport: "I don't think it will ever happen now.
"Roy [Hodgson] has four years and I hope he sees it out and has great success.
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"It saved me making a decision in all honesty because I'm very happy at Tottenham. I wish Roy all the best. I'm fed up of hearing my name mentioned now, I'm history.
"I'm not bothered, I've got a great job and I'm lucky. There are lots of lads who are cleverer than me who are managing at lower division clubs.
"I'm lucky I'm managing a top four, top five club, one of the best in the country. I don't feel like anyone owes me anything."