The League One side produced a spirited performance at Loftus Road and took the lead through Marc McNulty, before Jamal Campbell-Ryce grabbed two goals in the second half.
Redknapp said: “They were brighter and better than us and looked like a team that had 10 days without playing a game ??? we were playing our fourth (in the same period) and looked lethargic. We looked sluggish today.
“They thoroughly deserved their win. They played well and you’ve got to give them the credit. Look at their record ??? they got to the semi-finals last year and this year are in the semi-finals of the Capital One Cup.???
While maintaining their Premier League status will be QPR’s key aim this season, their cup record of just two wins in 23 games makes dismal reading for all at the club.
He added: “It’s no good shouting and screaming. What can you do? Our home form has been fantastic. But we didn’t play well today and the third goal summed us up. That was a horrendous goal.”
Campbell-Ryce???s second came when he took advantage of Leroy Fer???s wayward headed clearance.
Meanwhile, United continued a run of success in cup competitions that has seen them defeat Aston Villa, West Ham and Southampton over the past couple of years.
The Blades face Tottenham Hotspur in the semi-final of the Capital One Cup later in January and first-team coach Chris Morgan doesn???t expect the Premier League side to take them lightly.
He said:??”Everybody in the semi-final draw would have wanted to play us. The Premier League clubs would want to avoid each other, it’s just the nature of the beast.
“But I don’t think people will take us lightly, because of the results we’ve had. In the last calendar year we’ve beaten five Premier League clubs.
“The semi-final will be different in that it’s over two legs. But with the atmosphere and the type of performance we can get at home, we know if we’re still in the tie when we get back to Bramall Lane then there will be a game on.
“We had a great run (in the FA Cup) last year, getting to the semi-final, and this year we’ve backed that up with some really good performances. We were confident but when you come away to Premier League sides you’ve got to work hard and get the blocks in like we did.
“We know we can come and compete with top teams. It’s great to have a run in the cup ??? great for supporters and for the revenue of the club.”