City's second-half surge proved decisive, with Nico O'Reilly, Marc Guehi and Jeremy Doku all finding the net to keep the visitors firmly in the title race.
For Chelsea, the result left them sixth in the Premier League, four points behind Liverpool in the chase for a top-five finish and Champions League qualification.
Rosenior did not hide his frustration, pointing to familiar issues that have plagued his side in recent weeks.
"Not good enough in the second half," he said. "It's a similar story for the past month in terms of dealing with setbacks.
"When you go behind against a team like this, you have to stay in the game. Instead, it became a really difficult second half."
The defeat marked Chelsea's fifth loss in six matches across all competitions, including three straight league defeats without scoring. Supporters voiced their anger at full-time, but Rosenior accepted responsibility.
"I am accountable," he said. "There wasn't a lack of effort, but there was a lack of confidence in the second half. We have to improve quickly because we are in a difficult place."
Off the pitch, the absence of Enzo Fernandez continued to draw attention. The midfielder missed a second successive match after being suspended following comments about a potential summer exit.
Rosenior confirmed the situation had been addressed internally.
"Any team will miss Enzo," he explained. "The decision was made for the long term of the club. He has spoken with me and the players, and there is nothing personal. He will return to the group this week."
Chelsea's focus now shifts to a crucial clash against Manchester United at Stamford Bridge on 18 April, a match that could define their fading hopes of securing Champions League football.
