And after playing his strongest possible side against Championship strugglers Posh in Saturday's third-round tie, he vowed to do the same all the way to Wembley.
Redknapp said: "I put a good team out to win the game. You don't want to take liberties and winning is a good habit. I didn't want to put a weak team out and turn in a sloppy performance and then regret it afterwards."
On being asked whether Tottenham could win the cup this year for the ninth time in their history, Redknapp said: "We've got a chance the same as all the big boys. We have a good squad and there was no reason for me to mess about too much today.
"We're not in Europe. We only have two competitions. It would be different if we were involved in a Carling Cup semi-final like Aston Villa and Blackburn or Manchester United and Man City. But I have no reason to rest anybody for next Sunday, it's a week away.
"Every game is important. There was a full house here. People paid good money to come and watch the game. It was important we turned in a good performance.
"It would be nice to see someone outside the big four win the cup again. There's a long way to go but I like the way we are playing. We moved the ball well and played the ball around the pitch quickly."
Two goals from Nico Kranjcar and the inevitable strike from Jermain Defoe put Tottenham in control as they dominated a one-sided cup tie.
Captain Robbie Keane completed the rout in injury-time when he slotted home from the penalty spot after substitute Danny Rose had been brought down by Chris Whelpdale.
It could have been worse but for some spectacular saves from Posh goalkeeper Joe Lewis, who is being tracked by Premier League clubs.
Peterborough manager Mark Cooper said: "The goalkeeper kept us in it in the first half. He didn't deserve to concede four goals with his performance
"We thought Harry might rest a few but it wasn't to be. It was a fantastic performance from them. I was really impressed. They are a really good team.
"He (Redknapp) probably wants to keep the continuity going and rightly so and they were too good for us today.
"I said to the players 'You are playing against some of the best in Europe today go and enjoy it, test yourselves.' I can't fault the effort from the players. We just didn't defend. The goals were too soft."
Cooper thought Peterborough deserved a penalty when substitute Shaun Batt was brought down by Michael Dawson before Tottenham were awarded theirs.
Cooper said: "For me it's a penalty but he waves it away and goes straight down the other end and because Peterborough are bottom of the league he can't wait to give it so 3-1 becomes 4-0."
As for Tottenham, Cooper believes they can win the cup and as for the league, added: "I think they will finish in the top four."