"[Manchester City] have gone away to Tottenham and Manchester United and got great victories, so we knew this was going to be an incredibly tough game for us because of the level," Rodgers told Sky Sports News.
"But really the focus is very much on our own game because we feel like if we can pass the ball and have the courage to play, we will hurt teams and that is something that we've proved over the last couple of seasons.
"Even against the best teams we believe that we can cause problems. Today was a great victory and a terrific goal to win the game."
The Swans have moved up to 11th in the table with the win.