Brightfield cell microscopy is a foundational tool in life sciences. The acquired images are prone to contain visual artifacts that hinder downstream analysis, and automatically removing them is therefore of great practical interest. Deep convolutional neural networks are state-of-the-art for image segmentation, but require pixel-level annotations, which are time-consuming to produce. Here, we propose ScoreCAM-U-Net, a pipeline to segment artifactual regions in brightfield images with limited user input. The model is trained using only image-level labels, so the process is faster by orders of magnitude compared to pixel-level annotation, but without substantially sacrificing the segmentation performance. We confirm that artifacts indeed exist with different shapes and sizes in three different brightfield microscopy image datasets, and distort downstream analyses such as nuclei segmentation, morphometry and fluorescence intensity quantification. We then demonstrate that our automated artifact removal ameliorates this problem. Such rapid cleaning of acquired images using the power of deep learning models is likely to become a standard step for all large scale microscopy experiments.