Deciphering the complex interactions between neurotransmission and astrocytic $Ca^{2+}$ elevations is a target promising a comprehensive understanding of brain function. While the astrocytic response to excitatory synaptic activity has been extensively studied, how inhibitory activity results to intracellular $Ca^{2+}$ waves remains elusive. In this study, we developed a compartmental astrocytic model that exhibits distinct levels of responsiveness to inhibitory activity. Our model suggested that the astrocytic coverage of inhibitory terminals defines the spatial and temporal scale of their $Ca^{2+}$ elevations. Understanding the interplay between the synaptic pathways and the astrocytic responses will help us identify how astrocytes work independently and cooperatively with neurons, in health and disease.