Computer-aided diagnostic methods that provide semantic segmentation of texture patterns of diffuse lung diseases (DLDs) on chest computed tomography (CT) are extremely useful for detecting, identifying, and quantifying lung pathologies. While a fully annotated dataset is desirable to build a semantic segmentation model, building such a dataset for DLDs is costly due to the requirements of manual segmentation and certified experts for annotation. Partially supervised learning (PSL) has been proposed recently to take advantage of the partially annotated dataset and reduce the full annotation burden. Creating a partially annotated dataset is much less expensive than creating a fully annotated dataset. Therefore, PSL has great potential to build a semantic segmentation model that only requires a feasible amount of annotation. In this study, we propose a method of PSL employing a loss function that uses both annotated and unannotated pixels of a partially annotated dataset. The proposed loss function is based on the cross entropy loss, and it uses unannotated pixels to penalize the leakage of the segmentation. A parameter that controls the balance between the two types of supervision is introduced into the loss function to allow tuning and studying of the proposed PSL. The effectiveness and characteristics of PSL for the segmentation of DLD classes (consolidation, ground grass opacity, honeycombing, emphysema, and normal) were investigated in experiments using chest CT images of 372 patients. The experimental results show that the proposed PSL improved the mean Dice score from 0.76 to 0.79, and that a higher value of the balancing parameter increased the precision of the segmentation. Using the proposed PSL, which takes full advantage of the partially annotated dataset, we improved the accuracy of DLD segmentation. Furthermore, the experimental results clarified that the proposed PSL improved the precision of the models using unannotated pixels. Our implementation of the proposed PSL is available at https://github.com/yk-szk/psl-dld.