The Reds took the lead in the first half thanks to Fabinho’s fine long-range strike, and Mohamed Salah made it 2-0 to the hosts before half-time.
Sadio Mane then made it 3-0 to Jurgen Klopp’s men in the second half, before Bernardo Silva pulled a goal back for the visitors.
The victory lifted Liverpool FC eight points clear at the top of the Premier League table, with Manchester City dropping down into fourth spot.
BBC Sport pundit Crooks singled out Fabinho for special praise after the game but also praised Liverpool FC for their impressive all-round performance.
Writing in his column for BBC Sport, Crooks said: “Liverpool’s performance against Manchester City was about as professional as you will ever see from a Premier League team.
“Manchester City played the football and Liverpool got the job done. They were absolutely ruthless.
“This was not a game for the stars either but one for the unsung heroes. The men who do all the running, never complain and seldom get the headlines. The Hendersons, Wijnaldums and my man of the match Fabinho.
“Was it a handball by Trent Alexander-Arnold – you bet your sweet life it was – but that was the break Liverpool needed and boy did they take advantage of it.”
Liverpool FC will return to Premier League action after the international break when they take on Crystal Palace away from home on 23 November.
The Reds are aiming to win the Premier League title for the first time this season after having finished just a single point behind Manchester City last term.
Liverpool FC are next in Champions League action with a home clash against Napoli on 27 November.
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