Luis Suárez scored twice in the opening 10 minutes to give the Reds a commanding lead before Daniel Agger headed a third goal for the visitors.
The Hoops did improve after the interval but Redknapp’s men were unable to beat Pepe Reina as the Reds helds on for three points.
The loss leaves QPR rooted to the bottom of the Premier League, eight points behind 17th-place Aston Villa after 20 games.
“It’s not easy getting players in at this stage at the bottom of the league, but if someone is up for the challenge, it’s a great chance,” Redknapp told BBC Sport.
“We need new faces and if we get the right players we can make a real effort. We have some hard games to come but there is a long way to go. You could have 10 games to go and need 20 points and it can be done.
“Don’t give up, we have to keep believing, keep going. Those that are with us are with us, those that aren’t, we’ll try and do something.”
Redknapp also defended his side’s performance, admitting Liverpool – and Suárez in particular – were just too good for QPR.
“It’s difficult,” he added. “It’s easy to sit there and say there’s no fight. It’s easy to say that. We got moved about by better players. Suarez… What can you do when he does that to Clint Hill?
“I think it’s easy to say it was a lack of effort. We started the season getting beat five by Swansea. You can only get the best out of what you’ve got.”
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