Screening effectively identifies patients at risk of sight-threatening diabetic retinopathy (STDR) when retinal images are captured through dilated pupils. Pharmacological mydriasis is not logistically feasible in non-clinical, community DR screening, where acquiring gradable retinal images using handheld devices exhibits high technical failure rates, reducing STDR detection. Deep learning (DL) based gradability predictions at acquisition could prompt device operators to recapture insufficient quality images, increasing gradable image proportions and consequently STDR detection. Non-mydriatic retinal images were captured as part of SMART India, a cross-sectional, multi-site, community-based, house-to-house DR screening study between August 2018 and December 2019 using the Zeiss Visuscout 100 handheld camera. From 18,277 patient eyes (40,126 images), 16,170 patient eyes (35,319 images) were eligible and 3261 retinal images (1490 patient eyes) were sampled then labelled by two ophthalmologists. Compact DL model area under the receiver operator characteristic curve was 0.93 (0.01) following five-fold cross-validation. Compact DL model agreement (Kappa) were 0.58, 0.69 and 0.69 for high specificity, balanced sensitivity/specificity and high sensitivity operating points compared to an inter-grader agreement of 0.59. Compact DL gradability model performance was favourable compared to ophthalmologists. Compact DL models can effectively classify non-mydriatic, handheld retinal image gradability with potential applications within community-based DR screening.