Beginning the day top of the Barclays Premier League, having lost just once at home and conceded five in six matches, they ended it in third place.
Sergio Aguero’s ninth of the season just before the break on his return from injury barely softened the blow with Reds defender Martin Skrtel brilliantly volleying home in the second half to complete the rout.
“I am more than angry, it is unbelievable the performance we had,” said Pellegrini. “I have never seen this team play in the way they did tonight.
“It was a complete disaster, the whole team.
“It is difficult to understand why we should play so badly – not just one name but a complete team in defending or attacking possession.
“I think we didn’t prepare – we lost so many balls in attack it was impossible to create chances, we conceded four goals and could have conceded at least three or four more.”
Pellegrini’s decision to leave out centre-back Nicolas Otamendi and midfielder Fernandinho, two of City’s most consistent performers recently, was questioned but the Chilean refused to expand on his team selection – or his reasons for substituting captain Yaya Toure and Jesus Navas at half-time.
“I will not explain the starting XI, if I had to choose the same starting XI again I would do,” he added.
“There are a lot of things why I took the decisions with the starting XI but there was not one thing.
“I was not happy with the performance of the 11 players, not just Yaya and Navas when I substituted them at half-time.
“We tried to make another system and press high but it was exactly the same, it was not our night.”
Pellegrini also refused to discuss the performance of Raheem Sterling on his first appearance against the club he left in the summer in a £49million deal.
“I don’t want to talk about one player,” he said. “These things sometimes happen in football, why we played so badly today – that is why I do not want to talk about one player or a tactical system.”
His biggest win since taking over seven weeks ago more than made up for the home defeat against Crystal Palace immediately before the international break.
“It was very satisfying. I’m not sure if it was the best (performance) but I rarely compare games,” Klopp said.
“Two weeks ago we lost the game against Palace, now we have taken those points back.
“For us it is important we can see and feel there is a development in our game. We need common experience so we can work with it.
“We can do better than we did tonight – maybe not on the counter-attack because they were really good but we can start to believe in our own strength.
“At half-time I had a little bit of a feeling some of them were feeling surprised we were in the lead here and that is what we have to learn.
“It is normal in football if you have quality – and we have quality – you can be in the lead.”
Klopp left £32.5million striker Christian Benteke among the substitutes, where Daniel Sturridge was named for the first time in Klopp’s tenure after recovering from injury.
The German selected the majority of players he had to work with at Melwood during the international break and the link-up play between Coutinho and Firmino certainly proved that was the right call with the latter particularly impressive.
“I told you a few weeks ago I know about his quality,” said Klopp of Firmino. “He trained 10-12 days with us without interruption, the same as Coutinho, and that is the reason we played like this with the formation like this – we tried to put on the pitch as many players who trained together.”
MAN CITY 1-4 LIVERPOOL