BRUSSELS — The operatic ouster of Rex Tillerson leaves a State Department angry and adrift, and a world even more confused about the management and direction of American foreign policy, hoping but not expecting that the change leads to greater coherence in Washington.

The angst is being felt especially acutely among European leaders. With the back-to-back resignation of Gary Cohn, Mr. Trump’s top economic adviser, and the firing of Mr. Tillerson they fear the period of “benign neglect” they have experienced so far from Mr. Trump is over.

Mr. Tillerson was roundly criticized by a much-demoralized diplomatic corps, accused of gutting budgets and staffing levels in a reflection of what many see as a long, downward trajectory of the State Department’s influence.

But for allies, in particular, he was also seen as “one of the grown-ups” and a relative voice of reason, even comfort, in comparison with his boss’s brash impulsiveness.