Redknapp was fired by Spurs in June after almost four years in charge. In that time he guided Spurs to a first-ever Champions League campaign in 2010 and fourth-place finishes in the Premier League in two of the last three seasons.
He returned to management in late November. Rangers are deeply embroiled in a battle for Premier League survival, propping up the standings after 21 games and five points adrift of safety.
"I can't lie and say my four years at White Hart Lane meant nothing. I don't think anyone would believe me anyway," Redknapp wrote in his column in The Sun newspaper on Friday.
"It was a special time for me and for the club. But now I've gone I'm not the sort to bear a grudge - I pity people that do, in fact.
"I'm 65 now and where is that going to get me? Nowhere, fast. Life does move on. That is football. I have not got a problem with anyone at Tottenham, for sure."
Redknapp said he had no problem with Levy and "would shake his hand, no problem".
He added: "On the day I started at QPR, the first call I got was from Daniel wishing me luck.
"What's happened has happened and is in the past. He is the chairman, he decided he wanted a change of direction with regard to the manager and that's that.
"I thoroughly enjoyed my time at Spurs but now my focus is to get three points for Rangers when we play them.
Rangers, winless when Redknapp replaced the axed Mark Hughes on November 24, have just two victories under Redknapp, including a shock 1-0 win at Chelsea in their last league game on January 2.
They host third-placed Spurs at Loftus Road and Redknapp said he believed his old side were capable of winning the Premier League "within a season or two".
"I left behind a fabulous group of players at Spurs," he said. "The manager now, Andre Villas-Boas, has added a couple of names to that and look at them go."
Rangers announced on Friday that former Nottingham Forest manager Steve Cotterill had agreed a short-term coaching role to "assist Harry Redknapp and his backroom team".
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