Manager Harry Redknapp has said that bottom-placed QPR need to win up to five of their remaining eight games to avoid Premier League relegation.
QPR are now seven points from safety, but Redknapp refused to give up on maintaining their top-flight status.
"We need to win four or five games. It is not impossible. While there is hope, you keep believing," he told the BBC.
"It is hard with the points situation, but we cannot be playing any better. We are playing very well, that is all we can do.
"With eight games to go, we need to keep trying to win the games. If we can do that, we can still do it."
In a rollercoaster fixture at Villa Park, Redknapp's men took the lead when Jermaine Jenas followed up on a rebound from a Bobby Zamora shot.
Seconds after a Jose Bosingwa free-kick hit the woodwork, they then conceded an equaliser against the run of play as Gabriel Agbonlahor headed in unmarked.
Andreas Weimann gave them the lead but Andros Townsend's deflected shot levelled things up for the visitors. Villa then got the decisive goal when Christian Benteke slotted in his 13th league strike of the season unopposed.
"We could have been three or four goals up at half-time, it was that one-sided," Redknapp added. "Their goalkeeper [Brad Guzan] pulled off several world-class saves and then they break and score.
"They could not believe their luck coming in at half-time.
"In the second half, we did not start as well, and it gave them a lift. But even then, at 2-2 we gave a sloppy third goal away."
The result for Villa means that they have beaten relegation rivals in consecutive weekends after last weekend's triumph at Reading, in the process moving six points clear of the drop zone.
Prior to the clash with QPR, manager Paul Lambert had insisted he was not "unduly worried" about the prospect of dropping down to the Championship and the Scot remained confident of a strong end to the season.
"Last week's win was a big win for us," the ex-Norwich boss said. "It is now the first time since we have done it back-to-back since [May] 2011, so it is a long time since we have had that feeling.
"We are still fighting [to stay up], as are a lot of teams. We have pulled a few in it and we are playing very well at this time.
"If we keep this up, I have always said we will be OK."