The visitors dominated the first half and deservedly took the lead through Jermaine Jenas only for Gabriel Agbonlahor to equalise for Villa right on the stroke of half-time.
Villa went in front just before the hour mark through Andreas Weimann, but Andros Townsend hit back for QPR only for Christian Benteke to grab a priceless late winner for Villa.
Redknapp was at a loss to explain how his side had lost the game after missing several chances to go further in front in the first half before Agbonlahor's leveller.
"We should have been three or four goals up at half-time we were so much the better team it was almost embarrassing," Redknapp told Sky Sports.
"But they scored right on half-time, we have only got to keep the ball we are down in their corner, we have got them under pressure and they hit us on the break.
"They came in at 1-1 and I am sure they couldn't believe their luck because they should have been out of the game and that is how it went today.
"We get back to 2-2 and we still look the more likely team to win. I felt we were causing them problems.
"They have rode their luck today and good luck to them, they have got away with it. I am sure Paul (Lambert) would look at it and think that was a tough day. They could have been dead and buried at half-time, they should have been dead and buried.
"When you are losing you have got to keep chasing once we went behind, but how we were ever behind, we should have been out of sight by half-time."
The defeat leaves QPR rooted to the bottom of the table, seven points adrift of safety and Redknapp admits the result could have a big impact on their survival hopes.
"It's got a big bearing even if we come away 2-2 and take a point, but it's opened up a gap today and Southampton have won.
"It's going to be tough but we are still there, so who knows?
"We have got to keep playing; we are playing so well at the moment.
"I thought we were excellent, last week we were excellent against Sunderland, and against Southampton the week before. So we are in good form, we just need to win four or five games, we need to do it, it is not impossible we are playing well enough to do that."
Redknapp admits QPR probably need to win five out of their last eight games to have any chance of staying up and he is refusing to give up.
"It's hard to do when we have not won that many all year, but it's not impossible we are playing well enough to do it," he concluded.