Redknapp was the overwhelming favourite to take charge of the Three Lions' post vacated by Fabio Capello earlier this year but was overlooked in favour of Roy Hodgson.
The 65-year-old holds no grudges, though, telling the Daily Mail: "I was enjoying my life at Tottenham and I did wonder how I would cope, if it happened, with what is part-time football. I do enjoy seeing footballers every day; being on the training ground."
He continued: "I was driving when I heard on the radio that Roy had got the job. It happened out of the blue. But I didn't lose any sleep over it that night.
"I was almost quite relieved in a way - that I hadn't been given a decision to make. The decision had been taken away from me."
Although the Football Association have insisted Roy Hodgson was always their first choice, Redknapp hinted contractual matters with his then club Tottenham may have played a part in him being overlooked.
He said: "When I look back I think it was always going to be a problem for me. I mean, I have to be careful what I say here, but I had a contract that was very heavily loaded; that anyone who wanted to take me, we're talking massive money in compensation.
"The FA would say that it wasn't the reason and it wouldn't be fair on Roy Hodgson to say I would have had the job had it not been for that. But I always felt, from day one, that it might rule me out. That it might be a problem."
Redknapp guided Spurs to a top four finish in the Barclays Premier League last season and they only missed out on Champions League football by virtue of Chelsea winning the competition. Therefore it came as a surprise when the former West Ham, Southampton and Portsmouth boss left White Hart Lane over the summer, replaced by Andre Villas-Boas.
"Looking back I don't think finishing fourth decided it," Redknapp added. "I think the club just wanted to make a change. It was their decision. It was Daniel Levy's decision to do what he did and he can do what he wants. It's his club."
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- Roy Hodgson