The Reds prevailed 4-3 in a compelling Anfield encounter, inflicting a first league defeat of the season on City, days after Coutinho left the club to join Barcelona in a deal worth a reported £142 million.
Liverpool manager Klopp said: “It’s not that I said in a meeting, ‘Boys, it would help a lot if you could win tonight so nobody speaks about Phil Coutinho anymore’.
“We like speaking about him. He’ll still be jumping in his new living room in Barcelona, happy about the win tonight.
“But it was important to show we can play without him and we did that. That’s a very important statement.”
Liverpool took control with goals from Roberto Firmino, Sadio Mane and Mohamed Salah in a blistering nine-minute spell in the second half after Leroy Sane had cancelled out Alex Oxlade-Chamberlain‘s early strike.
Goals from Bernardo Silva and Ilkay Gundogan set up a nervy finish, but Liverpool held on.
Klopp, whose post-match press conference was bizarrely interrupted by an interloper asking him about his favourite type of cake, said: “You need a really good football team to do that [to City] and, thank God, I have one. They tried really hard today.
“It was just a joy to watch, how both teams threw everything on the pitch. It is a nice commercial for Premier League football.
“The whole world was watching. If someone didn’t watch football until now, now they’ll see why people watch it all the time. I’m really happy about it.”
City boss Pep Guardiola suggested his side struggled to deal with the raucous atmosphere inside Anfield as Liverpool took control.
Guardiola said: “My first words are congratulations to Liverpool for the victory. It was a good game.
“They started well. We lost a lot of balls because they are so aggressive without the ball and we had problems controlling that.
“After that we started to play much better and we have good chances, especially in the second half we started good—until the goal from Firmino.
“After that we lost a bit of control. We were involved in the environment of Anfield, for many reasons.
“You have to try to be stable and there are good lessons [to be learned], especially for the knockout stages of the Champions League.”
Guardiola had previously said his side would not go through the season unbeaten.
He said: “Losing is never good news, but all the teams lose games. It is important not to lose again.”
Guardiola refused to answer a question on continuing speculation linking his club with Arsenal‘s Alexis Sanchez, but did reveal Fabian Delph had suffered a knee injury and could be “out for a while”.
Regarding the Anfield atmosphere, Klopp said: “It was outstanding from the first whistle. It is one of the best places in world football if we are all on our toes.”