Two goals from Mario Gomez helped the German giants overcome a strong challenge by the English Premier League club.
Speaking after the match, Rummenigge had nothing but praise for his players.
"That was a good display and a great team performance, although Manchester City were also excellent in the first 30 minutes, when they showed what a good team they are. But in the second half we were totally on top of them," Rummenigge told the clubs official website.
Rummenigge also reserved special praise for Frank Ribery and Jerome Boateng.
"All the team played well, but Franck Ribery and Jerome Boateng were exceptional. We've put ourselves in a great position to qualify for the last 16."
The win puts Bayern top of Group A with six points.