Most convolutional neural networks (CNNs) for image classification use a global average pooling (GAP) followed by a fully-connected (FC) layer for output logits. However, this spatial aggregation procedure inherently restricts the utilization of location-specific information at the output layer, although this spatial information can be beneficial for classification. In this paper, we propose a novel spatial output layer on top of the existing convolutional feature maps to explicitly exploit the location-specific output information. In specific, given the spatial feature maps, we replace the previous GAP-FC layer with a spatially attentive output layer (SAOL) by employing a attention mask on spatial logits. The proposed location-specific attention selectively aggregates spatial logits within a target region, which leads to not only the performance improvement but also spatially interpretable outputs. Moreover, the proposed SAOL also permits to fully exploit location-specific self-supervision as well as self-distillation to enhance the generalization ability during training. The proposed SAOL with self-supervision and self-distillation can be easily plugged into existing CNNs. Experimental results on various classification tasks with representative architectures show consistent performance improvements by SAOL at almost the same computational cost.