The Mercedes driver finished behind Lewis Hamilton in Sochi to slip 17 points behind his teammate in the drivers' standings, although the one-two finish sealed a first Constructors' Championship triumph for the Silver Arrows.
"We are world champions! I feel so happy for the team and the whole Mercedes-Benz family, today we made history," Rosberg told reporters after the inaugural race in Russia. "I remember well the hard times we had in this team. So now it's great to be so dominant in our sport.
"But I'm also divided. Today was a really tough race for me. I just messed up in the first corner. I simply braked too late, which was unnecessary, so I flat spotted my front tyres and it was impossible to continue due to the vibrations. I had to pit, and on the prime tyre I had great pace.
"In the middle of the race I thought the degradation would start to increase. But very soon it was stable and I was able to push a lot. Then I managed to overtake Bottas. Also still at the end I was able to push, but the team asked me to control the pace as everyone was worried about dropping at the very end of the race. P2 was damage limitation."
Three races remain in the F1 calendar this season - United States, Brazil and Abu Dhabi.