Detecting emotions directly from a speech signal plays an important role in effective human-computer interactions. Existing speech emotion recognition models require massive computational and storage resources, making them hard to implement concurrently with other machine-interactive tasks in embedded systems. In this paper, we propose an efficient and lightweight fully convolutional neural network (FCNN) for speech emotion recognition in systems with limited hardware resources. In the proposed FCNN model, various feature maps are extracted via three parallel paths with different filter sizes. This helps deep convolution blocks to extract high-level features, while ensuring sufficient separability. The extracted features are used to classify the emotion of the input speech segment. While our model has a smaller size than that of the state-of-the-art models, it achieves a higher performance on the IEMOCAP and EMO-DB datasets. The source code is available https://github.com/AryaAftab/LIGHT-SERNET