Spurs won 2-0 at Anfield after a goal each from Rafael van der Vaart and Luka Modric.
Redknapp told Sky Sports: “We want to finish as high as we can. We want to finish fifth if we can and that would be great.
“We’ve had a great season. We had a great run in the Champions League and to finish fifth would be a great achievement from the players.”
Redknapp heaped praise on Ledley King after the game at Anfield.
“I took a real gamble today with Ledley, he was a little bit apprehensive about playing and I think wanted to leave it to the beginning of next season,” Redknapp explained.
“But I thought we needed to know sooner or later whether he was going to come back and play, and we pushed him into it a bit.
“But he is an amazing footballer when you think about it.
“He doesn’t train and then comes out and produces a performance like that, it’s amazing really.”
