Transoesophageal echocardiography (TEE) is a valuable diagnostic and monitoring imaging modality. Proper image acquisition is essential for diagnosis, yet current assessment techniques are solely based on manual expert review. This paper presents a supervised deep learning framework for automatically evaluating and grading the quality of TEE images. To obtain the necessary dataset, 38 participants of varied experience performed TEE exams with a high-fidelity virtual reality (VR) platform. Two Convolutional Neural Network (CNN) architectures, AlexNet and VGG, structured to perform regression, were finetuned and validated on manually graded images from three evaluators. Two different scoring strategies, a criteria-based percentage and an overall general impression, were used. The developed CNN models estimate the average score with a root mean square accuracy ranging between 84%-93%, indicating the ability to replicate expert valuation. Proposed strategies for automated TEE assessment can have a significant impact on the training process of new TEE operators, providing direct feedback and facilitating the development of the necessary dexterous skills.