The 27-year-old bagged his third treble of the season at Elland Road - taking his tally to 23 goals in all competitions in 2009/10 - to seal a 3-1 win and book a trip to Bolton Wanderers in the next round.
And afterwards manager Redknapp hailed his talismanic front-man, insisting that on current form Defoe is as deadly as fellow England forward Wayne Rooney.
“He could have had six, he had so many chances," he told the Mirror.
"He probably missed three easier chances.
“I signed him as a 15-year-old and used to watch him score every week. He is up there with Rooney, who is the best striker I have seen in years.
"It was a well deserved win. I was delighted with the way we played. We had lots of good chances."
Spurs opened the scoring against the League One promotion favourites through Defoe's 37th minute strike, but were pegged back by half-time following Luciano Becchio's leveller after Defoe had squandered several opportunites.
And the diminutive goal-getter revealed that he received a rollicking from striking coach Les Ferdinand at half-time for only scoring once.
“I can't say exactly what Les said to me at half-time, but basically he told me if I didn't get a hat-trick he would give me a boot up the backside," he said.
“I wasn't at all concerned when I missed those early chances because I knew the goals would come if I got into those scoring positions.
“It was satisfying to get my third hat-trick of the season, which puts me up there with Wayne Rooney.”
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