The Hoops put an end to City's perfect record under manager Pep Guardiola by claiming a 3-3 draw in the entertaining Champions League tie between the two clubs on Wednesday night.
Rodgers said: "Manchester City are one of the great clubs in the world and play in the most competitive league in the world and they're blowing everyone away.
"Yet we matched up and we showed that despite all the quality they have we weren't inferior.
"There were elements of the game we can learn from, of course, but it was a wonderful advertisement for the club but also for the nation.
"For me coming here it's about making the supporters happy, to make them proud of the team, to make the team aggressive. You have to represent them. You're wearing the shirt.
"If they stepped out of the stand they would give their life. They would be running up and down the pitch all day, tackling, fighting.
"On the pitch you have to create what happens in the stands and that's what the team is doing and the supporters are getting joy from watching them. We have to keep pushing them."