Significant progress has been made in self-supervised image denoising (SSID) in the recent few years. However, most methods focus on dealing with spatially independent noise, and they have little practicality on real-world sRGB images with spatially correlated noise. Although pixel-shuffle downsampling has been suggested for breaking the noise correlation, it breaks the original information of images, which limits the denoising performance. In this paper, we propose a novel perspective to solve this problem, i.e., seeking for spatially adaptive supervision for real-world sRGB image denoising. Specifically, we take into account the respective characteristics of flat and textured regions in noisy images, and construct supervisions for them separately. For flat areas, the supervision can be safely derived from non-adjacent pixels, which are much far from the current pixel for excluding the influence of the noise-correlated ones. And we extend the blind-spot network to a blind-neighborhood network (BNN) for providing supervision on flat areas. For textured regions, the supervision has to be closely related to the content of adjacent pixels. And we present a locally aware network (LAN) to meet the requirement, while LAN itself is selectively supervised with the output of BNN. Combining these two supervisions, a denoising network (e.g., U-Net) can be well-trained. Extensive experiments show that our method performs favorably against state-of-the-art SSID methods on real-world sRGB photographs. The code is available at https://github.com/nagejacob/SpatiallyAdaptiveSSID.