Interactive segmentation of 3D Gaussians opens a great opportunity for real-time manipulation of 3D scenes thanks to the real-time rendering capability of 3D Gaussian Splatting. However, the current methods suffer from time-consuming post-processing to deal with noisy segmentation output. Also, they struggle to provide detailed segmentation, which is important for fine-granular manipulation of 3D scenes. In this study, we propose Click-Gaussian, which learns distinguishable feature fields of two-level granularity, facilitating segmentation without time-consuming post-processing.We delve into challenges stemming from inconsistently learned feature fields resulting from 2D segmentation obtained independently from a 3D scene. 3D segmentation accuracy deteriorates when 2D segmentation results across the views, primary cues for 3D segmentation, are in conflict. To overcome these issues, we propose Global Feature-guided Learning (GFL). GFL constructs the clusters of global feature candidates from noisy 2D segments across the views, which smooths out noises when learning the features of 3D Gaussians. Our method runs in 10ms per click, 15 to 130 times as fast as the previous methods, while also significantly improving segmentation accuracy.