While Leeds may not be the force they were in the 1970s when Redknapp played for West Ham, the Spurs boss knows it will be no easy ride into round five and a clash at Bolton.
"Going to Elland Road can't be as intimidating as when they had Norman Hunter, Jack Charlton, Billy Bremner - that was one of the great football teams, right up there with the very best," Redknapp said.
"But it will be a tough game, they will be difficult opposition and played ever so well at White Hart Lane, even though we should have won the game.
"They are a team who can play way above their level, but we are doing well, with just two defeats in 12 games."
Spurs conceded a penalty deep into stoppage time as Leeds battled to a earn another crack at the Premier League side.
Redknapp's men were also hit by a late equaliser at Birmingham in their last match and the Spurs boss wants his men focus right until the final whistle.
"We played ever so well at Birmingham, we dominated the game and looked solid, but got caught in the last minute," he said.
"It is just a case of switching off from an attack, one of those things that happens."
With Robbie Keane having joined Celtic on loan, Redknapp confirmed centre-back Michael Dawson would step in as skipper again, given Ledley King will be rested.
"Michael Dawson has been captaining the team, and has done a good job," the Spurs boss said.
"He signed a new contract, has been in great form, a real leader who leads by example and so he will be captain the team against Leeds."
Striker Roman Pavlyuchenko (groin) is not expected to feature, while new signing Eidur Gudjohnsen is unavailable as he was not involved in the original tie.
With fellow new recruit Younes Kaboul and Kyle Walker, recalled from Sheffield United, both cup-tied, Redknapp admits the deadline day deals have left his options somewhat limited.
"We are one or two down in terms of numbers, but it will be an opportunity for a couple of youngsters to come and sit on the bench," he said.
"I will speak to (academy manager) John McDermott and (under-18s coach) Alex Inglethorpe to see which players deserve that opportunity."
Spurs arranged a friendly against a Dagenham & Redbridge side to give Gudjohnsen and Kaboul a chance to work on their match fitness ahead of the Premier League game at Aston Villa this weekend.
Redknapp said: "Eidur is just a fantastic footballer. I watched him yesterday, he sees the ball before it arrives.
"Younes, meanwhile, has the potential to make the French World Cup squad. He will do a fantastic job for us."
Tottenham 4/5, Draw 12/5, Leeds 10/3