John Achterberg and Daniel Hodges both admitted to their behaviour after things got heated during a Premier League clash on August 31.
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The incident came in the dying moments when Fabio Carvalho netted a winner in a 2-1 victory for Jurgen Klopp's side eight minutes into stoppage time.
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This led to outrage in the Magpies' camp given that just five minutes of injury time were signalled to be played.
Newcastle's head of performance Hodges, defender Fabian Schar and Liverpool's goalkeeping coach Achterberg put themselves in hot water
Achterberg was seen sticking two fingers up at the Newcastle dugout, while a bottle was allegedly thrown at the Liverpool bench.
The FA charged the pair, and have now released a statement.
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"Coaches from Liverpool FC and Newcastle United FC have been banned, fined and warned for breaching FA Rule E3 during their Premier League game on Wednesday 31 August 2022," the FA wrote.
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"John Achterberg and Daniel Hodges both admitted that their behaviour during the 98th minute was improper, and the Liverpool FC coach also accepted that he used abusive and insulting gestures.
"An independent Regulatory Commission has fined the Liverpool FC and Newcastle United FC coaches £7,000 and £6,000 respectively, banned them from the touchline for one fixture, and warned them as to their future conduct."