Nigel Clough's League One outfit, who reached the semi-finals of last season's competition and have also made the last four of this year's League Cup, brushed aside their hosts 3-0 at Loftus Road on Sunday.
While admitting that his side didn't deserve anything from the clash, Redknapp claimed that QPR's congested schedule was to blame for their lethargic showing.
"They were sharper than us all over the pitch and they were brighter and better than us," he said.
"They looked like a team that had a rest for 10 days and we looked like a team that had played four games in 10 days and the last goal and the second goal were really disappointing ones to concede and summed us up.
"We were sluggish, and they thoroughly deserved their win but I had to play four or five of them who have been playing recently but they had to play because there was nobody else."
United were able to withstand early pressure before taking the lead through top-scorer Marc McNulty in the 36th minute.
Impressive winger Jamal Campbell-Ryce then doubled their advantage four minutes after the restart, before sealing the victory in the last minute of stoppage time.
QPR therefore suffered a first home defeat in seven games and Redknapp, who won the FA Cup with Portsmouth in 2008, said: "We've been excellent at home up until today. I was very disappointed but what can you do.
"We've been good at home so I'm not worried. We've got Manchester United here next, and Burnley away next weekend which is massive for us.
"When you're playing every few days it makes it harder, but you have to deal with that, so you bring other lads in and you hope they do the job.
"We only started to play when [Eduardo] Vargas and [Mauricio] Isla came on in the second half – we played some football and looked brighter but I couldn't take any positives from today."
