Redknapp says the squad's confidence was not knocked by the 3-2 defeat by fellow strugglers Aston Villa before the international break despite it putting them seven points adrift of safety.
They make the short trip to Fulham on Monday night and, with eight games stilll to play, Redknapp believes his side is playing well enough to get out of the mire.
He said: "Obviously ourselves and Reading are in a difficult position but there are seven or eight other teams involved in it.
"I still feel we can get out of it and nothing has changed my belief. We played so well at Villa we could have come in at half-time three or four up. We've got to go on a little run now and get the results we need.
"If we were in bad form we'd be more worried. We're playing very well, we're in a good form so it gives us a chance.
"At least we're going into the last eight games knowing we're playing well. If we were going into it playing very poorly I'd be more worried. I still think there are four or five wins left in us."
Redknapp also backed Adel Taarabt to play a big part in their survival battle and rejected claims that he left the mercurial Moroccan out of the side recently because he lacked the stomach for their fight.
"Adel was fantastic when he came on against Villa and he is still very much in the frame," Redknapp added.
"We need Adel for the last eight games to be a part of what we are trying to do. People look at him and think he doesn't care but he does - I think he cares very much about we do.
"It's up to him. If he works hard with the ball and without the ball and does his job for the team, he's still got a big part to play."