Liverpool wrecked Manchester City's hopes of returning to the top of the Premier League and delivered more evidence of vast improvement under new manager Jurgen Klopp with an emphatic victory at The Etihad.

Klopp's side tore City apart with a dazzling first-half performance, which saw them take a 3-0 lead through Eliaquim Mangala's early own goal and cool finishes from Philippe Coutinho and Roberto Firmino.

Sergio Aguero gave City faint hope when he pulled a goal back on half time but City were undermined by shambolic defending as they failed to cope with the absence of injured captain Vincent Kompany.

Liverpool, however, never looked like conceding their advantage and Martin Skrtel's thunderous late fourth confirmed their superiority as they added this fine away win to their recent victory at champions Chelsea.

Klopp's revival continues

The optimism engendered by Klopp's arrival was punctured by Liverpool's home defeat by Crystal Palace, but all the signs of what the former Borussia Dortmund coach wants from his side were on show here.

Liverpool put City under pressure in possession right away and it was not long before City's impatient fans were getting stuck into their team for their inability to get the ball out of their own half.

The visitors were able to cut through City's defence almost at will, with Klopp urging his players not to take a backward step as they went in search of what would be a highly impressive victory.

The contrast between the two managers could not have been starker. Klopp was all action and animation in his technical area while City counterpart Manuel Pellegrini stood motionless for much of the match, hands in his pockets or with arms folded in frustration. The body language reflected the performances of their teams.

Coutinho and Firmino the key factors

Coutinho struggled to hit his previous heights earlier this season but the little Brazilian magician has come to life with the arrival of Klopp.

His equaliser right on half-time time at Chelsea paved the way for victory at Stamford Bridge and has reignited him. He was masterly as Liverpool cut City to shreds in the first 45 minutes, dropping deep into positions where he could not be countered then darting into the area to get a goal and create countless problems.

The same applies to £29m summer signing Firmino. He initially struggled with the pace of the Premier League after arriving from Hoffenheim but has grown in confidence backed by the faith of Klopp, who has started him in an advanced role in preference to Christian Benteke in the wins at Chelsea and now City. It is a ploy that has reaped a rich reward.

Can City cope with Kompany?

Aguero's absence is always a source of anxiety to Manchester City - but on this evidence the damage is even worse when Vincent Kompany is missing.

The injured City captain looked on grim-faced from the stands as Mangala and Martin Demichelis floundered - although they were by no means the only offenders in what was a shocking display from Pellegrini's team.

Without Kompany, City lacked authority and composure at the back and had Liverpool scored more they could have had few complaints.

Man of the match - Philippe Coutinho

What they said

Manchester City manager Manuel Pellegrini: "Today we did it all wrong - the performance, the way we defended, the way we went forward. It was a fake night, a fake game. It is difficult to understand.

"If we meant to do it on purpose we couldn't have done it that badly. We tried to make changes and have some options to score. We tried to fight but continued making so many mistakes with the ball."

Liverpool manager Jurgen Klopp: "It feels perfect. The game was not perfect but it was very good.

"City couldn't start like they want but that is important for us. We played with big passion and that's the most important thing for us.

"The good news is that we can do better. At half-time I told the boys they were surprised to be winning 3-0, and we must do better in that situation.

"We have quality, we could have more goals but 4-1 is perfect. The boys can believe now that they are stronger than many people think."

The stats you need to know

• This game saw Man City concede three goals in the first half of a competitive game at the Etihad Stadium for just the second time (2-3 v Manchester United in the FA Cup in Jan 2012, the other)
• This is only the second time that Man City have conceded four goals in a competitive game at the Etihad (Man City 2-4 Aston Villa in the League Cup in September 2012 the other)
• It's the first time they have conceded four at home in the Premier League since February 2003 against Arsenal. That game, at Maine Road, ended 5-1
• Sergio Aguero became the top-scoring South American player in Premier League history (85 goals)
• Liverpool have scored as many goals in their last two away Premier League games (7) as they managed in their 11 before that

What's next?

Manchester City travel to Juventus in the Champions League on Wednesday. Group leaders City lead the second-placed Italians by a point.

Liverpool are also in Europe, but in the Europa League on Thursday when they face Bordeaux at Anfield. Klopp's side are second in Group B, three points ahead of the French side and two behind leaders FC Sion.