Visual explainability for object detection remains challenging due to the multi-instance nature of detection. Existing approaches predominantly adopt post-hoc paradigms, such as gradient-based or perturbation-based explanation methods, to interpret pretrained detectors. However, these methods require additional gradient computation or repeated model inference, resulting in limited efficiency. To address this issue, we propose an End-to-end Instance-specific Visual Explanation framework (EIVE) that directly generates instance-level saliency maps following the forward pass of Detection Transformer (DETR)-like models. Specifically, we reformulate the cross-attention mechanism in the decoder as an instance-level feature attribution pathway, so that the cross-attention of each object query corresponds to the visual attribution of its predicted instance. Based on this formulation, we design a cross-layer hybrid consensus fusion (CLHCF) module to aggregate cross-attention signals across decoder layers, producing stable and compact explanations. The explanation process of EIVE requires neither gradient computation nor input perturbation, yielding high computational efficiency, and applies to single- and multi-scale DETR-like object detectors. Finally, we present an attention-aware joint training strategy (AAJTS) as a training-oriented application, which imposes spatial constraints on cross-attention patterns to encourage stable and concentrated attribution representations, thereby improving both interpretability and detection performance. Experiments on MS COCO 2017, ExDark, and Cityscapes demonstrate that EIVE produces high-quality instance-level saliency maps and achieves performance comparable to, or better than, state-of-the-art post-hoc methods across standard metrics, while substantially improving explanation efficiency. Code is available at https://github.com/xjlDestiny/EIVE.git.