It took the visitors four minutes to shake the Liverpool net, courtesy of a goal by Leandro Trossard.
Liverpool defeated Ajax 2-1 at Anfield to record their first victory in the competition.
Fabio Carvalho found the back of the net from 3 yards after seven minutes of injury time, even though the referee had signalled for five.
Liverpool thrashed Bournemouth 9-0 at Anfield to secure their first three points of the season.
Liverpool piled on the pressure from the blast of the whistle but Palace who lost their season’s opener to Arsenal remained resilient.
The Reds came for a revenge having lost last season’s Premier League title to City.
Nonetheless, the ‘Reds’ keep their head high as they ended the season as the only unbeaten side in the Premier League in 2022.
A win for Manchester City will see Liverpool return to second position on the EPL log, with three points behind City.
Klopp’s extended stay is also likely to influence the thinking of a number of players who are entering the final 12 months of their contracts.
Liverpool on Tuesday slipped to a shock defeat against Inter Milan at Anfield but managed to seal their place into the Champions League quarterfinals.
