This paper proposes a distributed control scheme to compensate for droop-induced frequency deviations in autonomous microgrids. In this scheme, no extra direct frequency control and proportional-integral compensation are employed to remove the frequency deviations; that is, the deviations are compensated instantaneously. To reduce the communication burden, the scheme is then equipped with a need-based (event-triggered) data exchange strategy. An event-triggering mechanism is introduced, which highly reduces the amount of communications in both transient and steady-state stages and ensures that the intervals between consecutive communication instants are positive (i.e., the system is Zeno-free). Stability and equilibrium analyses of the resultant system considering the whole system dynamics are provided, as well. Effectiveness of the proposed controller for different cases is verified by simulating a microgrid in MATLAB/SimPowerSystems software environment.