Zinchenko played a key role in City's win and said manager Pep Guardiola's side are ready to go to the wire in the tightest title race for years.
“It was a big performance from the lads," said Zinchenko. “We played well, a bit lucky, because we scored with almost every single chance at the beginning of the match.
"But I think that's more about hard work in training sessions and not so much about luck.
“Everyone involved in our team is ready to play against Chelsea and these kind of teams.
“It was a big game and we prepared well. We played like a real family.
“Everyone who is playing here knows every game is so tough. We have to keep going in this way.
“We have to have full focus on our game now. I hope Liverpool are going to drop some points in the next game. But first we have to focus on us.
“Hopefully we can win every title. We're going to fight for every one of them. Hopefully we can win all four trophies."