Sterling reached 50 goals for the club after scoring a brace that helped City to a dominant triumph, with Sergio Aguero, David Silva and Leroy Sane also among the goals.
The win moved City two points clear of Liverpool, who were held to a 1-1 draw by Arsenal on Saturday, and Sterling was pleased to take advantage after his former club slipped up.
"After Liverpool dropped points it was important that we won. They are a brilliant side," the England forward told BBC Sport.
"I thought it was a great team performance. Not just with the ball. We were brilliant at times."
Sterling unselfishly squared for Sane in second-half stoppage time to allow the Germany international to score City's sixth, and he said the winger often does the same in return.
"Leroy is always a man who looks up for me," said Sterling. "He always has his eyes open. I was on a hat-trick, but I am happy to set one up for him.
"I am grateful for the position I am in, learning and trying to get better. It is great times at the moment."
Sane's goal was his third of the season and his second in three Premier League matches, but he admitted there was an element of luck involved.
"I was lucky at the end with the goal," said Sane.
"I tried to score in the game, but the whole team was really strong.
"You can see we're keeping going with how we play from last season, we enjoy playing together. It was important to be top."