Automatic machine classification of concrete structural defects in images poses significant challenges because of multitude of problems arising from the surface texture, such as presence of stains, holes, colors, poster remains, graffiti, marking and painting, along with uncontrolled weather conditions and illuminations. In this paper, we propose an interleaved deep artifacts-aware attention mechanism (iDAAM) to classify multitarget multi-class and single-class defects from structural defect images. Our novel architecture is composed of interleaved finegrained dense modules (FGDM) and concurrent dual attention modules (CDAM) to extract local discriminative features from concrete defect images. FGDM helps to aggregate multi-layer robust information with wide range of scales to describe visuallysimilar overlapping defects. On the other hand, CDAM selects multiple representations of highly localized overlapping defect features and encodes the crucial spatial regions from discriminative channels to address variations in texture, viewing angle, shape and size of overlapping defect classes. Within iDAAM, FGDM and CDAM are interleaved to extract salient discriminative features from multiple scales by constructing an end-toend trainable network without any preprocessing steps, making the process fully automatic. Experimental results and extensive ablation studies on three publicly available large concrete defect datasets show that our proposed approach outperforms the current state-of-the-art methodologies.