The victory brings Pep Guardiola's side, who had drawn at Newcastle United on Saturday, back within eight points of leaders Liverpool ahead of the Merseyside derby with Everton at Anfield on Wednesday.
"That is not good enough", he said. Of course, it is not good for us.
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"He won't be ready for the derby", Guardiola told reporters. "They attack really well and, in defence, they are so aggressive".
Jurgen Klopp and his Liverpool team will still see them as a major threat, and rightly so. Sometimes the club wants to try to do the best but sometimes we can not. We have to think about what we have to do to win the games and play quite similar to recent games, especially like Newcastle and, except for 20-25 minutes, against Chelsea. And as soon as we lose that desire to win and think it's done then it definitely is done.
Sergio Aguero, Aymeric Laporte and Leroy Sane are out for the Burnley clash with injury, while Guendogan is suspended, having racked up five yellow cards. Their lengthy absentee list could tip the balance in favour of the hosts.
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Charlie Taylor is an injury doubt after being forced off against Palace while Johann Berg Gudmundsson is not yet fit after a hamstring problem. But, in Chris Wood and Ashley Barnes, they have one of the most-potent strike duo in the top flight.
Aguero got the victor on their previous visit to Turf Moor towards the back end of last season with a scrappy finish that barely crossed the line but put City within two wins of their second consecutive Premier League title. The Clarets have scored six of their goals from set plays this season.
Argentina worldwide Aguero picked up a thigh injury during City's 2-1 victory over Chelsea on November 23 and subsequently missed Saturday's draw at Newcastle. "If we have to hustle and bustle and shove and barge, so be it".
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Lionel Messi won the 10th La Liga title of his career last season scoring 36 goals and providing 13 assists in 36 top-flight for Barcelona .
It is still far too early to be ruling City out of the title race, given their ability to string together a relentless run of wins.