Schizophrenia is associated with diverse cognitive deficits, including disorders of attention-related oculomotor behavior. At the structural level, schizophrenia is associated with abnormal inhibitory control in the circuit linking cortex and thalamus. We developed a spiking neural network model that demonstrates how dysfunctional inhibition can degrade attentive gaze control. Our model revealed that perturbations of two functionally distinct classes of cortical inhibitory neurons, or of the inhibitory thalamic reticular nucleus, disrupted processing vital for sustained attention to a stimulus, leading to distractibility. Because perturbation at each circuit node led to comparable but qualitatively distinct disruptions in attentive tracking or fixation, our findings support the search for new eye movement metrics that may index distinct underlying neural defects. Moreover, because the cortico-thalamic circuit is a common motif across sensory, association, and motor systems, the model and extensions can be broadly applied to study normal function and the neural bases of other cognitive deficits in schizophrenia.