While the 2-1 loss still left them in third place, the chasing pack – both Manchester teams and Arsenal – have matches in hand which means the Reds can now be caught.
Fifth-placed United are only three points behind with two matches in hand, but even the Gunners, boosted by booking an FA Cup final place, will find encouragement in closing a nine-point gap with the three additional games they have to fit in.
Klopp, however, is adamant their destiny remains in their own hands. “I know there are a lot of people around thinking, ‘Oh my God, Champions League slips through our fingers again’, but only if we let it slip,” he said.
“We have to try everything and we will try everything. Our job is to squeeze everything out of the season we can squeeze.
“Obviously it is not easy for us, that is not a surprise.”
Former Liverpool striker Christian Benteke returned to haunt his old side on his return to Anfield, a ground he loves scoring on as an opposition player, netting both goals to turn around a game which had begun with Philippe Coutinho‘s brilliant free-kick giving the hosts the lead.
Benteke’s double took his tally against the Reds to seven in eight matches and he has one more goal at Anfield as an opposition player (five) then he managed during the 12 months he played for them there last season. Klopp, however, was unhappy with the way his players made it all too easy for him.
“Christian Benteke is an outstandingly good striker, absolutely no doubt about it,” said the German, who sold the striker in the summer.
“But if you leave him alone like we did for the first goal I am not sure he needed all his skills for this goal. It makes no sense to leave him alone.
“For the second goal just one player reacted and that is our mistake.”
Palace boss Sam Allardyce, who celebrated his first league win at Anfield, has guided the club to the brink of safety after accumulating 38 points thanks to some remarkable recent results against Arsenal, Chelsea and now Liverpool.
“I thought we were, from start to finish, tactically exceptional,” he said. “With our limited possession we exposed Liverpool’s weaknesses time and time again and ultimately that has brought us from 1-0 down to win it.
“I give the players a huge amount of credit for the way they defended and how they exposed the weaknesses of Liverpool defensively, which in the end they couldn’t cope with.”