The League One side stormed into a 4-0 lead inside the opening 56 minutes at Loftus Road after Armand Traore’s own goal, and strikes from Ryan Lowe, Ryan Harley and Darren Potter.
The west London side did manage to restore some pride, with Jay Bothroyd and Fabio Da Silva netting in the final 10 minutes, but were unable to save their unbeaten record in 2013.
The Hoops manager has only signed Loic Remy from Marseille this month despite being linked with a host of players, and the 65-year-old insisted the Premier League’s basement club must bring in new recruits.
“Surely they’re entitled to beat a team from two divisions down? It tells me I need to improve the squad,” Redknapp said.
“That is why I have gone all over Europe these last three weeks trying to improve the squad because we are short.”
Redknapp was also critical of his QPR side for losing to a club which is two tiers below the Loftus Road outfit, succumbing to the heaviest loss of his reign.
“If you look at the team today, what is it? An England goalkeeper [Rob Green], a right-back from Manchester United [Fabio], a left-back in Armand Traore,” he added.
“You’ve got Anton Ferdinand and Tal Ben Haim, then Esteban Granero from Real Madrid. You’ve got Ale Faurlin, Park Ji-sung from Manchester United, Jamie Mackie, Jay Bothroyd and DJ Campbell.”