Hundreds of social workers and volunteers are working round the clock, providing essentials to those affected by the unprecedented rainfall
Jurgen Klopp's side are on a seven match unbeaten run that includes five wins and has lifted them up to third place in the Premier League.
The Reds are sixth points clear of fifth placed Manchester United, who have two games in hand, as the race to reach Europe's elite club competition enters the final furlong.
The most encouraging thing for Reds boss Klopp is his team appear to have learnt how to grind out victories, as demonstrated by last Sunday's 1-0 win at West Bromwich Albion.
Liverpool have found life difficult against physical sides for much of the season, and have been particularly vulnerable when defending set-pieces.
For both of those reasons, they were expected to struggle at The Hawthorns, yet were rarely troubled by their opponents.
Such discipline will be required once more against a Palace side who have beaten Chelsea and Arsenal since the beginning of April.
Klopp has made clear that the quality of football is less important now than securing the wins that will ensure a top-four finish.
Liverpool have had to do that without their leading scorer Sadio Mane, whose season has ended early as a result of the knee injury sustained during the 3-1 victory over Everton on April 1.
They have also missed the influence of captain Jordan Henderson, whose foot injury means that he has not played since February 11.
Asked about Henderson's chances of playing again this season, Klopp said: "I don't know. We will have to see. He cannot really train so we have to wait for when he can.
"That was always the plan with the medical department. He is not patient any more, I can tell you that. He looks really healthy but nothing has changed."
With Mane and fellow injury victim Adam Lallana absent, Liverpool will continue to rely on Roberto Firmino, Philippe Coutinho and Divock Origi to lead their attack.
Firmino has scored the winner in each of Liverpool's last two matches, while Coutinho has contributed goals in three of his last four appearances.
Elsewhere, Klopp has several defensive injury concerns.
Joel Matip and Lucas Leiva have been unable to train this week because of muscle problems, while Ragnar Klavan has a minor medial knee ligament injury.
Joe Gomez could make his first Premier League appearance of the season, having fully recovered from cruciate knee ligament damage suffered in October 2015.
Palace have strengthened their chances of avoiding relegation with an impressive run that has brought five wins and a draw in their last seven league games.
However, they will be without Mamadou Sakho for the trip to Anfield with the on-loan centre-back ineligible to face his parent club.
James Tomkins is fit again and will replace Sakho and Allardyce is convinced Palace's recent run of results will strengthen their belief at Anfield.
"We're in Champions League form for picking points up, which should give us a huge amount of confidence on Sunday," he said.
"Hopefully we can be good enough, big enough and brave enough, and confident enough to try and repeat what we've done (in impressing) against Chelsea and Arsenal recently."
Christian Benteke will lead the Palace attack, and hope to extend a scoring run that has brought three goals in the last four games, on his first return to Liverpool since his disappointing 12-month stay was brought to an end last year.
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