Despite the significant advancements in its treatment, cardiovascular disease remains a major cause of illness and death globally, including Indonesia, creating a major financial drain. To support the identification of this disease, biomedical image segmentation, including cine cardiac MRI, is increasingly being used to automatically extract important functional parameters from MRI scans of the heart. Convolutional neural networks (CNN), particularly the U-Net architecture, have become popular for this task. However, traditional max pooling operations used in CNNs for image segmentation can lead to the loss of spatial information and sensitivity to small changes in the input image, potentially limiting the network's generalization ability. To address these limitations, this paper proposes an optimized modified U-Net neural network model with a fuzzy pooling layer extension. The fuzzy pooling considers all values within a pooling region, assigning weights based on their distance from the maximum value to preserve spatial information and reduce sensitivity to small input changes. Based on the experiment, the fuzzy pooling technique outperforms the max pooling technique for cine cardiac MRI image segmentation. The fuzzy pooling technique resulted in higher IoU values of 93.429% for End-Diastole and 85.802% for End-Systole, and smaller Hausdorff distance of 3.0 for End-Diastole and 3.1622 for End-Systole, indicating better accuracy. The proposed approach is expected to improve the effectiveness of automated image segmentation for diagnosing cardiovascular disease, which ultimately leads to better outcomes for patients.