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.
"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."