Inspired by the observation that humans are able to process videos efficiently by only paying attention where and when it is needed, we propose an interpretable and easy plug-in spatial-temporal attention mechanism for video action recognition. For spatial attention, we learn a saliency mask to allow the model to focus on the most salient parts of the feature maps. For temporal attention, we employ a convolutional LSTM based attention mechanism to identify the most relevant frames from an input video. Further, we propose a set of regularizers to ensure that our attention mechanism attends to coherent regions in space and time. Our model not only improves video action recognition accuracy, but also localizes discriminative regions both spatially and temporally, despite being trained in a weakly-supervised manner with only classification labels (no bounding box labels or time frame temporal labels). We evaluate our approach on several public video action recognition datasets with ablation studies. Furthermore, we quantitatively and qualitatively evaluate our models ability to localize discriminative regions spatially and critical frames temporally. Experimental results demonstrate the efficacy of our approach, showing superior or comparable accuracy with the state-of-the-art methods while increasing model interpretability.