The west Londoners go into the new year eight points adrift of safety, with just one victory to show from 20 Premier League outings this season.
"I think we'll stay up still," the Rs boss said. "You'll think we're mad, but I think we will stay up."
He added: "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, I don't need them around me.
"I need people who are upbeat. 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."
On Sunday they fell to a fifth home defeat of the season thanks to a Luis Suarez brace and a Daniel Agger header inside 27 minutes.
QPR would have hoped to have gained a slight advantage over Liverpool given they were without manager Brendan Rodgers. The Reds boss missed the game after being taken ill in London, with back-up goalkeeper Brad Jones and head of performance Glen Driscoll also sent home with the bug.
"Brendan picked the team. All the preparation for the game was all done," assistant manager Colin Pascoe said. "The presentations that we do to the players, that was all set. But unfortunately Brendan woke up and wasn't very well."
Source: PA
Source: PA