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The Champions League defeat came on the back of their 2-1 loss at Bournemouth, which allowed Liverpool to take over at the top of the Premier League, and their Carabao Cup exit at Tottenham Hotspur.
City were stunned by incoming Manchester United boss Ruben Amorim's side at the Jose Alvalade Stadium on Tuesday, slumping to a third successive defeat after a hat-trick by former Coventry striker Viktor Gyokeres.
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It was also Pep Guardiola's team's first reverse in the Champions League excluding a penalty shoot-out since 2022.
"Everything looks to be going in the wrong way.
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"Even when we are playing well we don't score our chances and we concede too easily.
We are not in the dark side.
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"We played really bad against Bournemouth but really good here.
I won't give up, that's for sure."
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City will move back top of the Premier League with victory at Brighton in the 5.30pm kick-off.
Liverpool then host Aston Villa in the 8pm kick-off at Anfield.
City had dominated the early proceedings in Lisbo n and looked like they could win comfortably after Phil Foden pounced on a mistake to open the scoring after four minutes.
The game turned when Gyokeres, who has been tipped to follow Amorim to Old Trafford, broke clear to level and the Swede added two more from the spot after Maximiliano Araujo put Sporting ahead.
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City's frustration was compounded when Erling Haaland missed a penalty.
It made for the perfect send-off for Amorim, who was taking charge of his final home match before officially starting work at United next week.
Amorim, who took a long lap of honour after the game, said: "Those who were here and have seen Sporting over the last four years deserved a night like this.
It was very special.
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"But we shouldn't stop here, it shouldn't be a one-off.
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