She rushed out of the room in a fluster.

Literal

She [topic-は] flustered-and room [from-を] left-and-went.

慌てる ('to be flustered, panic, hurry') in te-form 慌てて serves adverbially: 'in a fluster, hurriedly.' The verb captures both physical haste and a slightly disorderly mental state. 部屋を出る uses を to mark the location vacated — same path/origin construction as 家を出る. The directional ~ていく adds outward motion away from the speaker. Together, 慌てて出ていった depicts not just leaving but bolting in disarray.