Artificial Intelligence (AI) methods and technologies have been successfully applied for recognizing objects, detecting and segmenting RGB images. Today, such technologies are widely used in precision agriculture to estimate food quality, especially when assessing plants and fruits at various harvest stages. There are also several processes taking place in food during the postharvest stages, such as decay and moldy. However, the number of AI approaches allowing for assessing the postharvest food conditions is limited. In this work, we trained U-Net and Deeplab models based on Convolutional Neural Networks (CNNs) to detect and predict decay areas in postharvest apples stored at room temperatures. The models were trained on a dataset that includes 4440 images of apples with segmented decay areas. Images were captured by a digital camera mounted on a custom-made testbed. We achieved 99.71% of the mean Intersection over Union (mIoU) at the testing stage for the U-Net model and 99.99% of the mIoU at the testing stage for the Deeplab model trained on 651 images. We also presented the first masks for decay areas in apples predicted by U-Net. Our approach seems to be promising for improving the food storage process in precision agriculture by enabling the automatic detection and quantification of the decayed areas.