Liverpool pinned Palace back in the closing stages but could not force an equaliser as Palace held on to win at Anfield for a third successive season.
But their profligacy proved their undoing and Palace punished them, with Benteke providing Jurgen Klopp a costly reminder of his talents with the winning goal 16 minutes from time, giving Allardyce's side a huge boost and leaving Liverpool's top four hopes a little less certain.
The Reds still sit third in the standings, but have played two games more than fourth placed Manchester City and fifth placed Manchester United, while they have played three more games than seventh placed Arsenal.
But, former Liverpool defender Jamie Carragher was not feeling so hopeful after seeing former Red Christian Benteke score a brace to stun the hosts. We had the chances.
Here's the thing, though: I likely wouldn't be so mad if the goals Liverpool conceded weren't so avoidable.
Manchester United will not be surprised to hear that a Liverpool player won't be backing them considering the rivalry between the two clubs. Just two friends who are playing for the same team and who have the same goal, which is to get the three points at each game to make sure the team stays in the Premier League. We were dominant, you can not create 20 chances in a game like this, you have to work and that is what we did.
"You don't like it but there's a reason for them - not only what you did in the game, but also how you react after the game".
However, with captain Jordan Henderson, forward Sadio Mane, Daniel Sturridge and Danny Ings and defender Ragnar Klavan all now sidelined Jurgen Klopp's squad is looking threadbare.
With five wins in their previous seven games, The Eagles travelled to Merseyside in great form, but fell behind when Philippe Coutinho whipped a superb long-range free kick into the corner of the net.
Emre Can has said Liverpool need a flawless end to the season to secure Champions League qualification and a favour from Manchester City against Jose Mourinho's United on Thursday.
"But we have made a habit of upsetting the big teams and have done it again thanks to the big man". "We miss a lot of our players, there are a lot of injuries. We have to fight for our target".
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