Previously, we found that in the mammalian retina, inhibitory inputs onto starburst amacrine cells (SACs) are required for robust direction selectivity of On-Off direction-selective ganglion cells (On-Off DSGCs) against noisy backgrounds (Chen et al., 2016). However, the source of the inhibitory inputs to SACs and how this inhibition confers noise resilience of DSGCs are unknown. Here, we show that when visual noise is present in the background, the motion-evoked inhibition to an On-Off DSGC is preserved by a disinhibitory motif consisting of a serially connected network of neighboring SACs presynaptic to the DSGC. This preservation of inhibition by a disinhibitory motif arises from the interaction between visually evoked network dynamics and short-term synaptic plasticity at the SAC-DSGC synapse. Although the disinhibitory microcircuit is well studied for its disinhibitory function in brain circuits, our results highlight the algorithmic flexibility of this motif beyond disinhibition due to the mutual influence between network and synaptic plasticity mechanisms.