The demand for food delivery services (FDSs) during the COVID-19 crisis has been fuelled by consumers who prefer to order meals online and have it delivered to their door than to wait at a restaurant. Since many restaurants moved online and joined FDSs such as Uber Eats, Menulog, and Deliveroo, customer reviews on internet platforms have become a valuable source of information about a company’s performance. FDS organisations strive to collect customer complaints and effectively utilise the information to identify improvements needed to enhance customer satisfaction. However, only a few customer opinions are addressed because of the large amount of customer feedback data and lack of customer service consultants. Organisations can use artificial intelligence (AI) instead of relying on customer service experts and find solutions on their own to save money as opposed to reading each review. Based on the literature, deep learning (DL) methods have shown remarkable results in obtaining better accuracy when working with large datasets in other domains, but lack explainability in their model. Rapid research on explainable AI (XAI) to explain predictions made by opaque models looks promising but remains to be explored in the FDS domain. This study conducted a sentiment analysis by comparing simple and hybrid DL techniques (LSTM, Bi-LSTM, Bi-GRU-LSTM-CNN) in the FDS domain and explained the predictions using SHapley Additive exPlanations (SHAP) and Local Interpretable Model-Agnostic Explanations (LIME). The DL models were trained and tested on the customer review dataset extracted from the ProductReview website. Results showed that the LSTM, Bi-LSTM and Bi-GRU-LSTM-CNN models achieved an accuracy of 96.07%, 95.85% and 96.33%, respectively. The model should exhibit fewer false negatives because FDS organisations aim to identify and address each and every customer complaint. The LSTM model was chosen over the other two DL models, Bi-LSTM and Bi-GRU-LSTM-CNN, due to its lower rate of false negatives. XAI techniques, such as SHAP and LIME, revealed the feature contribution of the words used towards positive and negative sentiments, which were used to validate the model.