The England striker then grabbed a second in the 73rd minute from David Bentley's cross before completing his hat-trick at the end to earn Spurs a fifth-round meeting with Bolton.
Defoe told ITV1: "That was a difficult game. A cup tie is always difficult.
"Away from home it was a great performance from the lads, I am pleased with the win.
"We stuck in and still passed the ball."
David Bentley has had a difficult time at White Hart Lane since his move from Blackburn in July 2008, hardly featuring under Harry Redknapp.
The 25-year-old was voted man of the match despite Defoe's hat-trick and he told ITV1: "It has been a difficult time since I came here.
"I just look to every game I play, look to take advantage and enjoy myself. I take it game by game, you never know in football.
"My time at Tottenham has been a hard one but hopefully I can start enjoying it now."
Boss Harry Redknapp praised Bentley and challenged him to maintain his application, telling ITV1:
"He has come back and taken his opportunity.
"He has shown what a good player he is in the last couple of games and he needs to keep on doing that."
Of Defoe, Redknapp added: "He's got to keep working hard.
"They (Defoe and Peter Crouch) were a good pair tonight. It was a good all-found performance."
Leeds manager Simon Grayson was not too downbeat after the game and looked ahead.
He said: "We've just said to the players we've got to take a lot positives. We have given Tottenham two good games.
"Our main aim is to get promotion and play in front of 30,000 every week."