Monitoring surface cracks in infrastructure is crucial for structural health monitoring. Automatic visual inspection offers an effective solution, especially in hard-to-reach areas. Machine learning approaches have proven their effectiveness but typically require large annotated datasets for supervised training. Once a crack is detected, monitoring its severity often demands precise segmentation of the damage. However, pixel-level annotation of images for segmentation is labor-intensive. To mitigate this cost, one can leverage explainable artificial intelligence (XAI) to derive segmentations from the explanations of a classifier, requiring only weak image-level supervision. This paper proposes applying this methodology to segment and monitor surface cracks. We evaluate the performance of various XAI methods and examine how this approach facilitates severity quantification and growth monitoring. Results reveal that while the resulting segmentation masks may exhibit lower quality than those produced by supervised methods, they remain meaningful and enable severity monitoring, thus reducing substantial labeling costs. Code and data available at https://github.com/EPFL-IMOS/crack-explanations.