The European champions took a huge step towards a first top-flight title in 30 years by opening an eight-point lead at the top of the table, with Leicester City in second place.
Goals from Fabinho and Mohamed Salah gave Liverpool a dream start before Sadio Mané's diving header early in the second half sealed City's fate.
Bernardo Silva pulled a late goal back but a third defeat in eight league games leaves City down in fourth, nine points behind Liverpool, and with a mountain to climb if they are to claim a third straight league title.
"They (City) were good," Klopp told the BBC. "Oh they were good and we had to defend with all we had but we scored incredible goals".