Defoe's third treble of the season clinched the visitors a 3-1 win and a date at Bolton in the fifth round on the weekend of February 13-14. It also kept Spurs on course for their first FA Cup final since 1991.
Redknapp, who tasted FA Cup glory with Portsmouth in 2008, said: "It was nice to see him get his hat-trick. He could have scored six tonight in fairness. He had some great opportunities."
Defoe gave Tottenham a 37th-minute lead with a mis-hit shot that looped over Leeds goalkeeper Casper Ankergren and, although Luciano Becchio hauled the home side level in first-half stoppage time, Defoe struck twice more in the second period.
His decisive second, when he swept home David Bentley's cross, came in the 73rd minute and he coolly slotted home a third - his 23rd of the campaign - after rounding Ankergren in time added on.
Redknapp added: "He took three great finishes and missed three that were maybe easier, but he was always in the right place, he was always a threat. He's a goalscorer."
Redknapp, told earlier in the day his own horse, Arry's Orse, had won at Lingfield Park, had tipped Defoe to become a top-class goalscorer when he first saw him play.
The former West Ham and Pompey manager added: "He's always scored goals. I signed him as a 15-year-old and every Saturday I used to watch him in the youth team and he used to get hat-tricks, or score every week anyway. He's done it since he was a little boy."
Redknapp felt Leeds' equaliser was clearly offside and dealt a big blow to his players, coming just before the interval.
He said: "We had to pick ourselves up again for the second half, but when we kept the ball and passed the ball I thought we played well. Now we have another tough game at Bolton. It's not an easy place to go, but we're playing very well. We've had one defeat in 13 games."
Source: PA
Source: PA