Enabling robots to grasp disorganized cloth for efficient storage is valuable in robot-assisted room organization. Diverse deformations of cloth and the stacking of multiple items limit grasping-pose estimation that relies on annotations. This necessitates segmenting each cloth item in an unsupervised manner before estimating the grasping position. However, existing segmentation methods primarily focus on improving metrics such as Intersection-over-Union and Pixel Accuracy, which cannot effectively measure the segmentation errors of the cloth area and thus lead to failure grasping position estimation. To address this challenge, we use False Discovery Rate (FDR) as a novel measure of segmentation errors and analyze its impact on grasping success. Our preliminary study reveals a negative correlation between segmentation FDR and grasping success rate, highlighting the need for more reliable segmentation in cluttered cloth scenarios. Therefore, we propose an unsupervised cloth segmentation network based on feature distance-weighted constraints, designed to reduce the false discovery rate in cloth area perception without requiring expensive pixel-level manual annotations. Additionally, to estimate the grasping position on the perceived cloth area, we introduce a strategy based on cloth surface wrinkle analysis, which operates without the need for annotations or training. By integrating the proposed segmentation network and grasping strategy, we develop a robotic system capable of sequentially grasping cluttered cloth from a table. Extensive real-world robotic experiments demonstrate the effectiveness of our approach, outperforming multiple baseline methods in segmentation FDR and grasping success rate.