Autoencoders are a powerful and versatile tool often used for various problems such as anomaly detection, image processing and machine translation. However, their reconstructions are not always trivial to explain. Therefore, we propose a fast explainability solution by extending the Layer-wise Relevance Propagation method with the help of Deep Taylor Decomposition framework. Furthermore, we introduce a novel validation technique for comparing our explainability approach with baseline methods in the case of missing ground-truth data. Our results highlight computational as well as qualitative advantages of the proposed explainability solution with respect to existing methods.