The 65-year-old, who was cleared of tax evasion the day the Italian left the Three Lions job, led Spurs to fourth place for the second time in three seasons last term.
However, he insists he would not have wanted the "part-time" role and revealed he was delighted to hear Roy Hodgson had been approached.
"I was enjoying my life at Tottenham and I did wonder how I would cope, if it happened, with what is part-time football,” Redknapp told the Daily Mail. "I do enjoy seeing footballers every day; being on the training ground.
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"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."
The FA have since claimed that Hodgson was the only man they wanted and Redknapp believes contractual matters at Spurs could have influenced their decision.
"When I look back I think it was always going to be a problem for me," he added.
"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."
Chelsea’s triumph in the Champions League final last term denied Spurs a place among Europe’s elite this campaign, despite their fourth-placed finish.
But Redknapp has dismissed suggestions that this led to his subsequent sacking and the appointment of Andre Villas-Boas.
"Looking back I don't think finishing fourth decided it," he continued.
"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."