Interpretability, trustworthiness, and usability are key considerations in high-stake security applications, especially when utilizing deep learning models. While these models are known for their high accuracy, they behave as black boxes in which identifying important features and factors that led to a classification or a prediction is difficult. This can lead to uncertainty and distrust, especially when an incorrect prediction results in severe consequences. Thus, explanation methods aim to provide insights into the inner working of deep learning models. However, most explanation methods provide inconsistent explanations, have low fidelity, and are susceptible to adversarial manipulation, which can reduce model trustworthiness. This paper provides a comprehensive analysis of explainable methods and demonstrates their efficacy in three distinct security applications: anomaly detection using system logs, malware prediction, and detection of adversarial images. Our quantitative and qualitative analysis reveals serious limitations and concerns in state-of-the-art explanation methods in all three applications. We show that explanation methods for security applications necessitate distinct characteristics, such as stability, fidelity, robustness, and usability, among others, which we outline as the prerequisites for trustworthy explanation methods.