The Hoops boss felt they were unfortunate to go behind to Steven Fletcher's opener, but they hit back to seal victory thanks to goals from Loic Remy, Andros Townsend and Jermaine Jenas.
"It was a good performance to come from 1-0 down," he told Sky Sports.
"I felt we didn't deserve to be one down as we started well with a good tempo, we passed the ball well - better than I have seen us play since I came here, in an attacking sense.
"But to go one down against the run of play but to come back and equalise, I felt it was an excellent first half.
"In the second half they started well and for the first 10 to 15 minutes they were the better team, but we came back into it and got the goals at the right time.
"It was a great finish form Andros and another top-class strike from Jermaine Jenas - so the two Tottenham lads weighed in and it was a good performance all round."
Redknapp felt his whole team played well, but he says they need to now go on a run.
"I felt from Rob Green all the way out it, everyone played their part," he said.
"It was a good team performance, but we have to do that week in, week out and we have to have a real run of results like that if we are to get out of this, we need 36 or 37 points and that six points in two games has made a real difference to us.
"We have closed the gap and any team on 30 points is not safe. You can go
eight, nine or 10 games without winning quite easily.
"Anyone can have a bad run now and, if we continue to pick up points, we may
have a chance. It won't be easy but we have given ourselves a chance.
"I think there are a few teams above us who could get sucked in."
Redknapp is hoping to have Adel Taarabt, Julio Cesar and Armand Traore fit for the relegation run-in after the trio missed out against Sunderland due to injury.
But forward Bobby Zamora managed to play for 73 minutes before having to go off with hip and ankle knocks.
"Zamora wasn't really fit," said Redknapp. "He has done a miracle with his ankle ligaments.
"He is playing with an injury today when other players wouldn't have put themselves up to play.
"There are players not playing today with injuries that aren't as bad as Bobby's, that's for sure.
"You can only play what you've got, and this is the first time I've had Bobby and (Loic) Remy (up front). I liked the look of them."