The Brazil international, Liverpool's most potent creative force in the last fours seasons, joined the Spanish club for £142 million last week, but Klopp's team made light of his absence against the runaway league leaders.
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"It was the right statement," Klopp told a news conference. "It's not that I said in a meeting, 'boys it would help if you win tonight and no one speaks about Philippe Coutinho', because we like to talk about him actually. He's probably jumping in his new living room in Barcelona and will be happy about the win tonight. Of course, for us, it's important to show we can play without him and we did it, so that's a very important statement, absolutely."
England international Alex Oxlade-Chamberlain opened the scoring with less than 10 minutes played to kick-start a fluent Liverpool display and Roberto Firmino, Sadio Mane and Mohamed Salah struck in quick succession after the interval.
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City, who still lead second-placed Manchester United by 15 points, gave nearly as good as they got, with Leroy Sane getting a deserved equaliser just before halftime and Bernardo Silva and Ilkay Gundogan ensuring a nail-biting finish.
"It was just a joy to watch," said Klopp. "How both teams just threw everything on the pitch. Both teams tried to play football, without a lot of hard fouls. It's just a nice commercial for Premier League football. The whole world was watching it. If somebody didn't like football they would probably say, 'Oh, that's why you watch it all the time'."
Liverpool, whose win sent them third, could have been forgiven for adopting a conservative approach after being thumped 5-0 by City in the reverse fixture this season, but Klopp's plan to attack was vindicated.
"You have actually no alternative to beat City," he said. "Yes, you can win the lottery and they tackle each other or you can stand deep in your own box and hope nothing happens, but it's not likely.”
He added: “We are Liverpool and we should not try this way, to be honest. So you have no alternative. We needed to be brave, needed to play football. I'm really happy about that."
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