Mohamed Salah's 76th minute strike handed the Reds a priceless 1-0 win over Pep Guardiola's men.
However, Klopp was incensed that his goalscorer was not given an infringement late on and he reacted by berating assistant referee Gary Beswick for which he was shown a red card.
Klopp admitted afterwards that his behaviour was improper and was duly charged by the FA.
The former Borussia Dortmund manager has now learnt of his punishment, which he can appeal, but is likely to avoid a touchline ban.
"Jurgen Klopp has been fined £30,000 for breaching FA rule E3 during Liverpool FC's Premier League match against Manchester City FC on Sunday 16th October 2022," read an FA statement.
"The manager accepted that his behaviour during the 86th minute was improper, and an independent regulatory commission imposed his sanction during a hearing.
"This sanction is subject to appeal by either Jurgen Klopp or the FA following receipt of the independent regulatory commission's written reasons."
