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A wonderful first-half chip by Kun – his 199th goal for City – sent Pep Guardiola's side in 1-0 ahead against the Gunners at the break in the Wembley showpiece.
But rather than bask in the glory of the achievement, Sergio said the focus was already turning to Thursday night when City lock horns with Arsenal once again, this time at the Emirates in the Premier League.
The Blues will be looking to take another step towards securing the title in North London and to build on their 13-point lead at the top of the table.
"For me and for the team it is always a special trophy. We are happy and I am very happy," said Sergio.
"It's important for us as a team and for Pep and the club to win the Carabao Cup but now we want to keep going.
"We were better than them and we can celebrate. But now we have to focus on the next game away at Arsenal on Thursday and to think about the Premier League."
Sergio's goal came following a long kick upfield by goalkeeper Claudio Bravo with the Argentine striker then brushing off Skhodran Mustafi before calmly lobbing over keeper David Ospina.
Talking about the goal, Kun added: “For me there was no foul, a bit of a touch. I am happy because it was a goal.”
Celebrate the win with the Carabao Cup winners range.
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