Type 1 diabetes mellitus (T1DM) is characterized by insulin deficiency and blood sugar control issues. The state-of-the-art solution is the artificial pancreas (AP), which integrates basal insulin delivery and glucose monitoring. However, APs are unable to manage postprandial glucose response (PGR) due to limited knowledge of its determinants, requiring additional information for accurate bolus delivery, such as estimated carbohydrate intake. This study aims to quantify the influence of various meal-related factors on predicting postprandial blood glucose levels (BGLs) at different time intervals (15 min, 60 min, and 120 min) after meals by using deep neural network (DNN) models. The prediction models incorporate preprandial blood glucose values, insulin dosage, and various meal-related nutritional factors such as intake of energy, carbohydrates, proteins, lipids, fatty acids, fibers, glycemic index, and glycemic load as input variables. The impact of input features was assessed by exploiting eXplainable Artificial Intelligence (XAI) methodologies, specifically SHapley Additive exPlanations (SHAP), which provide insights into each feature's contribution to the model predictions. By leveraging XAI methodologies, this study aims to enhance the interpretability and transparency of BGL prediction models and validate clinical literature hypotheses. The findings can aid in the development of decision-support tools for individuals with T1DM, facilitating PGR management and reducing the risks of adverse events. The improved understanding of PGR determinants may lead to advancements in AP technology and improve the overall quality of life for T1DM patients.