Quantitative capillary-free zone (CFZ) analysis in optical coherence tomography angiography (OCTA) holds promise for the early detection of retinal diseases. However, its clinical deployment is hindered by time-consuming manual segmentation procedures for periarterial and perivenous CFZs, which often focus solely on large vessels. In this study, we introduce deep learning for the automated segmentation of periarterial and perivenous CFZs in OCTA. Both convolutional neural networks (CNNs) and vision transformers (ViTs) were evaluated for automated CFZ segmentation. Nine quantitative features were derived to characterize CFZ changes associated with diabetic retinopathy (DR). Quantitative analysis revealed significant changes in CFZ ratios, counts, and mean sizes that can reliably differentiate control subjects, diabetic patients without DR (NoDR), and those with mild DR, underscoring their potential as sensitive biomarkers for early disease detection, progression monitoring, and treatment assessment.