Spurs confirmed 65-year-old Redknapp's departure in the early hours of Thursday morning, with Everton's David Moyes and Wigan boss Roberto Martinez leading candidates to replace him, along with former Chelsea head coach Andre Villas-Boas and Rafael Benitez.
Redknapp, who has no intentions of retiring, felt the move was inevitable even if he had secured Champions League football, but maintained he left the club in a far better shape than when he took charge in October 2008.
"I leave behind some fantastic players. The only disappointment I have is that I think it was a team which could have gone on and eventually won the Premier league in the next year or two," Redknapp said.
"I just wish I could have been able to see that through and be part of that because they have some fantastic players there."
Martinez, who held talks with Liverpool over the summer, sidestepped the issue during a pundit stint for ESPN at Euro 2012, diplomatically stressing he was honoured to be linked to such a vacancy, and was testament to how well his Wigan side had performed.
Moyes has just returned from holiday and is also set to head out to the European Championships, so any face-to-face talks at White Hart Lane would have to wait.
Wigan chairman Dave Whelan insists there has been no approach for Martinez from Spurs, but would not block any potential meeting, as with sanctioning contact for Liverpool.
"If Tottenham come to me and ask to speak to him, I have to say the answer is yes. It always is," said Whelan, reported on BBC Sport.
"You cannot stop managers moving.
"Every club that people regard as a big club, when these jobs come up people say 'oh Roberto must be in for that'. And Roberto is actually quite happy at Wigan.
"I have not heard one thing from Tottenham Hotspur or from Roberto, so as far as I am concerned there is nothing going on at present.
"I just wait and see. Roberto is very happy, he is doing a brilliant job for me."
Whomever eventually replaces Redknapp, who not so long ago was the stand-out candidate for the England job, will be left in no doubt of what is expected by the White Hart Lane board.
Redknapp felt Thursday's outcome was always on the cards regardless of how the campaign ended, with Spurs losing out on Champions League football again despite finishing fourth in the Premier League, because of Chelsea's Champions League final triumph over Bayern Munich last month.
The former West Ham boss maintains he has no plans to retire and could now be set for a move overseas, with a long-standing offer of a coaching role in Dubai said to be on the table.
"I feel great. I don't feel any different. I love football. That is what keeps me going really. I am not one for sitting at home," he said.
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