Environmental Sound Classification (ESC) is an important field in a broad range of applications, such as smart cities, audio surveillance, and health care. Recently, Convolutional Neural Networks (CNNs) have taken the lead from traditional approaches and have produced promising results. However, the achieved improvements are often accompanied by increasing depth, complexity, and size of the network, which prevents their usage in many practical applications. In this work, our goal is to empower a small-size low-complexity CNN model to achieve superior performance. To this end, we concentrate on the importance of global pooling technique, which is less investigated in ESC. In most previous works, models utilize global average pooling layer which does not consider regional saliency, and thus weakens the salient time-frequency regions contributions to the classification, and also to the training of convolutional kernels. We propose a novel global pooling method, called Sparse Salient Region Pooling (SSRP), which computes the channel descriptors using a sparse subset of features, and guides the model to effectively learn from the more salient time-frequency regions. Experimental results demonstrate that the proposed model with only 700K parameters yields accuracies of 86.7% on ESC-50 and 94.8% on ESC-10, which are comparable to that of the state-of-the-art methods. Compared to the baseline model, our model achieves absolute improvement of 21.8% in accuracy on ESC-50, with 98% smaller model size. Our visual analyses show that SSRP intensifies the responses of low-energy regions such that they contribute even more than high-energy regions to the classification of specific sound classes.