Antonio Conte’s side have now lost twice in seven games this season and already sit six points behind their Manchester rivals.
Chelsea travel to face Crystal Palace after the international break, with Roma visiting Stamford Bridge four days after.
“We knew from the start it would be a tough match and we wanted to give our all, but not everything went well, like it did against Atletico,” Rudiger said.
“We have to keep our heads held high, come back after international duty and start again.
“Against Man City it’s not always easy, especially on the wings because they have quality players. We have a lot of quality as well but they had one shot which made the difference.
“Of course everyone is very disappointed. We had a very good month until this game. It was tough but every game in this league is tough.”
Rudiger’s Germany face qualifiers against Northern Ireland and Azerbaijan, with the Berlin-born defender hoping to add to his 19 caps.
The German is one of 11 of Chelsea’s first-team squad on international duty, however Alvaro Morata has withdrawn from Spain duty following an injury picked up against the Citizens.
With Danny Drinkwater already injured, the Blues will be hoping their players return in good shape as they now face a run of six games in 17 days before the end of October.
“First of all I hope everybody stays healthy, that’s the main thing, and then after we have to set our minds straight and go back on a winning run,” the defender said.
“We have to win against Crystal Palace, it won’t be an easy match but that’s the only way you can get back on track.”
