For the most part, we connect with the vast power of the two days of Rosh Hashanah through tefillah. It was up to her to daven to Hashem — for He, and only He, could bring about her salvation. She failed to recognize that she must rely only on Hashem, not the tefillos of another. Only after the sar hamashkim fails to deliver on this request does Yosef turn to Hashem as his only hope. They davened with the realization that Hashem, and only Hashem, can help them.