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Victory moved City two points clear at the top and Sane believes the performance was further evidence that Pep Guardiola’s reigning champions have kicked on from last season.
Sane, who also struck the post with a superb shot, said: "I was lucky at the end with the goals, I tried to score in the game, but the whole team was really strong today.
"You can see we're keeping going with how we play from last season, we enjoy playing together. It was important to be top today."
Team-mate Raheem Sterling, who produced a man-of-the-match display and scored twice, selflessly set up Sane for his goal sacrificing the chance to claim a hat-trick.
But he said he was happy to contribute for the team rather than seek personal glory.
"Leroy is always a man who looks up for me. He always has his eyes open. I was on a hat-trick but I am happy to set one up for him,” said Sterling.
"I am grateful for the position I am in, learning and trying to get better. It is great times at the moment.
"After Liverpool dropped points it was important that we won today. They are a brilliant side."
Today's starting XI, possible formation and various stats and milestones...