Pep Guardiola’s side returned to Premier League action following the two-week international break in imperious fashion at the London Stadium.
But despite the impressive manner of the win, Sterling revealed the City players were still not satisfied.
“All I can say is we want to get better. We want to improve. It’s a new season, we need to be on top of our game,” said Sterling.
“I thought at times we did some very good stuff. But at times we could have been better. Great win but at the same time a lot to improve on.
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“We gave them too many chances. On another day if they had took them, it could have been more difficult.
“We know what we done last year and it’s easy to be complacent. He (Pep) wants to keep us at a high level.
“We are trying to be better, do our best. That’s what will take us to the next level. Every day we need to perform and win games.
“There’s great competition, the other teams are doing well. We need to not be complacent, and to keep improving.”
Sane also dovetailed superbly with Sterling, setting up the England winger for City’s second goal before Sterling returned the favour for Sane’s first goal.
And Sterling said: “We’ve got a great understanding. When I see him (Leroy) on the ball, I can guess what he’s going to do.”