It was only the England winger's fourth goal following his August transfer from Arsenal and it couldn't have been more well-timed with Coutinho's exit having opened up a place in the team.
"It was just a joy to watch", Klopp said.
Leroy Sane had cancelled out Oxlade-Chamberlain's opener - and substitute Bernardo Silva and Ilkay Gundogan scored in the last six minutes to set up a thrilling finale. Liverpool leapfrog Chelsea into third spot.
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"Maybe it is an historic day", said Klopp. "I really think we deserved it".
WHICH stars make our combined Liverpool and Manchester City XI?
"The pressing in and around the box in the second half was from a different planet. outstanding", added Klopp. We needed to be courageous, needed to play football.
City remain 15 points clear at the top, though second-placed Manchester United have a game in hand - against Stoke on Monday. With city's unbeaten run in the current campaign, this match presents Liverpool full of their ambition to puncture City's tyres en route to the league title.
In fact, some of their defensive frailties were laid bare here which will not only give their domestic rivals hope but those concerned about them in the Champions League.
Manchester City manager Pep Guardiola confirmed Fabian Delph is likely to be out "for a while" with a knee injury as he counted the cost of Sunday's 4-3 defeat at Liverpool.
"You lose today against a fantastic team".
The Brazil global, Liverpool's most potent creative force, joined the Spanish club for 142 million pounds ($195 million) last week, but Klopp's team made light of his absence against the runaway league leaders. He was outmuscled by Firmino for a goal in this game and was also caught out in the win against Bristol City by forwards prepared to run at him. Now analyse and be positive.
"People asked if everything was over and done before Christmas, and now it's January and it's not", Guardiola said. We have a lot of games and hopefully we can stay fit in the schedule of games every three days.
During and after the game the reaction was one of wonder and amazement at what had just transpired.
BC-SOC-Liverpool-Man City, 2nd Ld-Writethru, 732 City's unbeaten run in EPL ends with 4-3 loss at LiverpoolAP Photo PDJ143, PDJ144, PDJ140, PDJ151, PDJ149Eds: Updates with details, quotes.
In other words - just about the ideal package for the neutral observer.
Nevertheless the home side has the ability and the guile to break the duck as they possess one of the best attacks in the Premier League.