Redknapp - who made Nugent available for transfer a matter of weeks after his £6million arrival from Preston this summer - said: "He needed a goal really and it was nice to see him notch.
"Hopefully David will come on from this. He needs to work hard and take his chances when they come. We've got a bit of competition up there because Kanu has been fantastic and I have got four up front."
Nugent's goal was greeted with strong Clarets protests as the home side protested he had handled the original pass from Pedro Mendes before firing the ball home.
And Burnley boss Steve Cotterill claimed Nugent had admitted the handball. Cotterill said: "Apparently he said to Steve Jordan it was handball.
"He said it but he could have been saying that to wind Steve Jordan up so we take it with a pinch of salt. It's certainly nothing we're going to be bleating about."
Redknapp shrugged off the incident, insisting he did not have a clear view, and instead paid tribute to his side which featured 10 changes with only Sylvain Distin keeping his place.
Redknapp added: "We were okay in the first half and in the second half we kept the ball quite comfortably. It's always difficult when you make 10 changes and put another team out.
"We've had a good week. We came up here for two tough games and we won them both. If we get a good result on Saturday it will have been a fantastic start to the season for us."