Redknapp was appointed on Saturday morning and left Mark Bowen in charge for the trip to Manchester United that afternoon, where they lost 3-1.
The trip to the Stadium of Light was the former Spurs manager's first in charge of Rangers, and he says there were plenty to make him believe that they can escape relegation.
"It was a good performance, there were a lot of positives tonight," he said.
"I feel more optimistic than I did on Saturday, I must be honest. I thought tonight was good for us.
"Confidence is key in anything you do. That's the key, I've got to keep encouraging them. It's no good knocking anybody. When you are bottom of the league your confidence is low.
"What you are relying on now - there's a group who have travelled all this way tonight from London to support the team and we've got to give them something to get behind.
"QPR reminds me of my time at Portsmouth. The fans were very similar, great supporters, same kind of stadium - small stadium - and if they really get behind us on Saturday I think the team can respond.
"I think we can become difficult to beat at home. We've got to win some games obviously but we've got to make the home form count - and the fans will play a big part in that."