The 66-year-old lamented his side's missed chances as the home side equalised just before half-time before scoring a late winner to leave the Hoops seven points from safety
The Hoops had the better of the first half and opened the scoring through Jermaine Jenas, but Christian Benteke would score a late winner to leave the Hoops rooted to the bottom of the Premier League.
"We looked so much the better team it was almost embarrassing in the first half," Redknapp told Sky Sports. "We should have been 3 or four goals up at half time.
"They scored right on half time - we only had to keep the ball. We were down in their corner and had them under pressure, and they hit us on the break.
"They came in at 1-1 and I'm sure they couldn't believe their luck because they should have been out of the game.
"We got back to 2-2 and we still looked the more likely team to win - I thought we were causing them problems. They rode their luck and I'm sure Paul Lambert will think it was a tough day."
Villa went ahead through Andreas Weimann on the hour and although Andros Townsend equalised, Benteke's late goal allowed the hosts to claim the relegation six-pointer and climb out of the bottom three.
"When you're losing you've got to keep chasing it - we had to once we went behind," Redknapp continued. "But I don't know how we ever went behind. We should have got a second and been out of sight by half-time."
Southampton's victory over Liverpool combined with the result at Villa Park leaves QPR seven points adrift of safety but Redknapp refused to give up on his side's chances of survival.
"It's got a big bearing on the rest of the season obviously - it would have even if we had taken a point and came away at 2-2," he admitted. "It's opened up a gap today, with Southampton winning as well.
"It's going to be tough, but we're still there - who knows. We are playing so well at the moment. Today I thought we were excellent, and last week we were excellent against Sunderland, and Southampton the week before.
"We just need to win four or five games. Out of eight it's hard to do when you haven’t won that many all year, but it's not impossible, and we're playing well enough to do it."