Ramsey's side looked set to move above Villa and out of the bottom three when Charlie Austin put them 3-2 up with 12 minutes to play at Villa Park on Tuesday.
But Benteke then curled home a brilliant free-kick to complete his treble and snatch a point for the hosts after a pulsating clash.
Matt Phillips opened the scoring early on at Villa Park, before Benteke struck twice to put the home team ahead at half-time.
Clint Hill's header levelled matters shortly after the break, and Austin put QPR in front with a typical poacher's finish before Benteke's superb intervention seven minutes from time.
A disappointed Ramsey told BBC Sport: "The goals we gave away were schoolboy errors.
"The point was better for them, we would have loved to have won the game and been above the line.
"Based on the performance in the second half we are disappointed we have not got three points."
Ramsey admitted Villa had the better of the first half but felt his team deserved more than a draw.
"In the first half we got overrun a bit, we caused our own problems our technique was poor, they had a lot chances and we rode our luck," he added.
"But we were fantastic in the second half and the travelling fans had something to cheer about."
