In speech emotion recognition (SER), using predefined features without considering their practical importance may lead to high dimensional datasets, including redundant and irrelevant information. Consequently, high-dimensional learning often results in decreasing model accuracy while increasing computational complexity. Our work underlines the importance of carefully considering and analyzing features in order to build efficient SER systems. We present a new supervised SER method based on an efficient feature engineering approach. We pay particular attention to the explainability of results to evaluate feature relevance and refine feature sets. This is performed iteratively through feature evaluation loop, using Shapley values to boost feature selection and improve overall framework performance. Our approach allows thus to balance the benefits between model performance and transparency. The proposed method outperforms human-level performance (HLP) and state-of-the-art machine learning methods in emotion recognition on the TESS dataset.