The west Londoners are bottom of the Premier League and five points adrift of safety, but were given a chance to get a morale-boosting win against npower League One opponents.
However, MK Dons had no interest in that script, progressing to the fifth round with a 4-2 win that made a mockery of the fact QPR were 31 places higher coming into the game.
With Manchester City coming to Shepherd's Bush on Tuesday, Redknapp chose to make nine changes and believes the only reason that backfired is because his players failed to perform.
"If you look at the team, what is it? An England goalkeeper [Rob Green], a right-back from Man United [Fabio], a left-back in Armand Traore," the QPR boss said.
"You've got Anton Ferdinand and Tal Ben Haim, then Esteban Granero from Real Madrid. You've got Ale Faurlin, Park Ji-sung from Man United, Jamie Mackie, Jay Bothroyd and DJ Campbell.
"Surely they are entitled to beat a team from two divisions down? It tells me, like I've said all along, that I need to improve the squad.
"That is why I have gone all over Europe these last three weeks trying to improve the squad because we are short.
"We are bottom of the league because that is where we are. We have picked up in the last 10 games or so, picking up 11 points, and we're getting blood out of stone at the moment.
"I know we need to improve and that is what we will continue to try and do this week, but it is not easy."