Due to the existence of low-textured areas in indoor scenes, some self-supervised depth estimation methods have specifically designed sparse photometric consistency losses and geometry-based losses. However, some of the loss terms cannot supervise all the pixels, which limits the performance of these methods. Some approaches introduce an additional optical flow network to provide dense correspondences supervision, but overload the loss function. In this paper, we propose to perform depth self-propagation based on feature self-similarities, where high-accuracy depths are propagated from supervised pixels to unsupervised ones. The enhanced self-supervised indoor monocular depth estimation network is called SPDepth. Since depth self-similarities are significant in a local range, a local window self-attention module is embedded at the end of the network to propagate depths in a window. The depth of a pixel is weighted using the feature correlation scores with other pixels in the same window. The effectiveness of self-propagation mechanism is demonstrated in the experiments on the NYU Depth V2 dataset. The root-mean-squared error of SPDepth is 0.585 and the δ1 accuracy is 77.6%. Zero-shot generalization studies are also conducted on the 7-Scenes dataset and provide a more comprehensive analysis about the application characteristics of SPDepth.