The newly-promoted Swans were undone by goals from Edin Dzeko and David Silva, while City debutant Sergio Aguero stole the headlines with two goals following his move from Atletico Madrid.
However, Rodgers has remained upbeat and insisted that he has faith in the way his side plays.
"I was very proud of the club," the manager told Sky Sports News. "It's a historic night, to demonstrate and show how we play was very good.
"I thought the result was harsh on our team. Certainly for the first hour we showed some great confidence on the ball and looked like we could be a real threat.
"Some of these players have been playing in League Two and came up through the leagues. To play with such quality was big for them.
"Our game is to construct from behind - I have big confidence in how we play."
Swansea's second Premier League fixture will see Wigan Athletic visit Liberty Stadium on Saturday.