While pap test is the most common diagnosis methods for cervical cancer, their results are highly dependent on the ability of the cytotechnicians to detect abnormal cells on the smears using brightfield microscopy. In this paper, we propose an explainable region classifier in whole slide images that could be used by cyto-pathologists to handle efficiently these big images (100,000x100,000 pixels). We create a dataset that simulates pap smears regions and uses a loss, we call classification under regression constraint, to train an efficient region classifier (about 66.8% accuracy on severity classification, 95.2% accuracy on normal/abnormal classification and 0.870 KAPPA score). We explain how we benefit from this loss to obtain a model focused on sensitivity and, then, we show that it can be used to perform weakly supervised localization (accuracy of 80.4%) of the cell that is mostly responsible for the malignancy of regions of whole slide images. We extend our method to perform a more general detection of abnormal cells (66.1% accuracy) and ensure that at least one abnormal cell will be detected if malignancy is present. Finally, we experiment our solution on a small real clinical slide dataset, highlighting the relevance of our proposed solution, adapting it to be as easily integrated in a pathology laboratory workflow as possible, and extending it to make a slide-level prediction.