The Londoners go into the new year eight points away from safety, with just one victory from 20 Barclays Premier League outings.
Liverpool romped to a 3-0 away victory, thanks to a Luis Suarez double and a Daniel Agger header in 27 minutes.
Redknapp said: "I think we'll still stay up.
"You'll think we're mad, but I think we will stay up.
"I only want positive people around me, I said that in the dressing room.
"Those that are moping around, the subs that are not playing are not playing because they're no good.
"If they had been any good, I'd be picking them. I don't need miserable faces around me.
"The next two games are unbelievable, Chelsea away and Tottenham at home, two of the best teams in the country.
"They are difficult games, but we've got to keep going and I still think we'll do it."
Redknapp promised not to "give up" on his side, although he accepts they deserved to lose yesterday.
"The first half was difficult but second half I thought we did okay," he said.
"They've got better quality than us. It was a very difficult game."
Redknapp needs reinforcements next month if QPR are to beat the drop, but was coy when asked about new faces.
"I'm not sure," he said. "If we can find the right players, get one or two in to make the difference.
"We need to get Bobby Zamora fit to give us a target up front. He could make a difference."
QPR would have hoped to have gained an advantage over Liverpool given they were without boss Brendan Rodgers.
The Reds boss missed the game having taken ill in London.
Assistant manager Colin Pascoe and coach Mike Marsh deputised at Loftus Road, although the former was ill himself.