Bottom-placed Rangers are now seven points adrift of the Premier League safety zone after Christian Benteke's 17th goal of the season finally settled a see-saw game in Villa's favour.
Rangers dominated the opening 45 minutes and deservedly led through Jermaine Jenas with only a string of fine saves from the Villa goalkeeper Brad Guzan keeping the home side in contention.
But Paul Lambert's side equalised on the stroke of half time through Gabriel Agbonlahor and went ahead through Andreas Weimann and, after Andros Townsend made it 2-2, Benteke struck the decider.
Redknapp said: "If we had come in 4-0 up half time it would have been about right wouldn't it? That's the best I've seen us play during that first half.
"It was so one-sided, it was unbelievable for an away team to dominate like that.
"But they got a lift from the equaliser after being absolutely awful first half and probably couldn't believe their luck. That goal knocked us for six.
"I'm upset for the lads. I thought they played so well today and we should have taken a point at 2-2 but then we gave away a bad goal."
Redknapp is refusing to throw in the towel in the battle for survival.
He said: "We've got to keep going. We can't go home and feel sorry.
"It's going to be hard but there are still eight games to go. If we keep playing well, we can win four or five games.
"We're probably looking at four wins and two draws. It's going to be hard but it's not impossible.
"I'm not giving up. We've still got to keep going."
Paul Lambert, the Villa manager, and the QPR assistant coach Joe Jordan exchanged words during the second half but Redknapp said: "It's no big deal. They'd have a row in an empty room."
Lambert was elated after the Midlands club achieved back-to-back Premier League wins for the first time in nearly two years.
He said: "Guzan has made three world-class saves and I will reiterate what I said before, that I wouldn't swap him for anyone.
"But I thought we passed the ball well and the goal rocked us.
"It will rock an experienced team when you lose a goal, not just a young team.
"But credit the team, we scored right at the death of the first half and after that we were exceptional.
"Is it the turning point of the season? I'm not so sure. There are eight games to go but we've got momentum there.
"There's a long way to go. What we have done is win back-to-back games for the first time since 2011 which is an incredible stat to have."
Weimann was voted the man of the match and he made a telling contribution with his goal and setting up the winner for Benteke.
Lambert said: "Andi Weimann is a phenomenal lad to work with. If he keeps his great enthusiasm for the game throughout his career, he'll have a big career for sure."
Rodriguez headed into the path of Morgan Schneiderlin to slot home the opener before Rickie Lambert doubled the advantage with his 13th goal of the season.
Philippe Coutinho reduced the arrears before Rodriguez made sure of the three points with 10 minutes remaining.
Stoke City 0 West Bromwich Albion 0
After Asmir Begovic kept out an early strike from the Albion captain Chris Brunt, the hosts – who went into the match having lost their last three league games and seven of their previous nine – were the better side in a scrappy first half.
The match improved after the break, but neither team could find a winner.
Swansea City 0 Arsenal 2
Arsenal kept themselves firmly in the race for Uefa Champions League qualification with a comfortable win at Swansea.
Nacho Monreal’s first goal for the club gave Arsenal the lead with 16 minutes remaining, before the substitute Gervinho struck in stoppage time.
Swansea faded badly after a promising opening but barely troubled Lukasz Fabianski in the Arsenal goal.
Manchester United 1 Reading 0
Wayne Rooney’s goal earned Manchester United victory over managerless Reading as they moved 15 points clear at the top of the Premier League.
The striker fired in with the help of a deflection off the Reading defender Alex Pearce in the 21st minute after Rio Ferdinand’s run forward set it up.
The England international Rooney fizzed over late on in the match in what was a laboured performance from United.
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