Interactive microservices expose API endpoints to be invoked by users. For such applications, precisely estimating the resources required to serve specific API traffic is challenging. This is because an API request can interact with different components and consume different resources for each component. The notion of API traffic is vital to application owners since the API endpoints often reflect business logic, e.g., a customer transaction. The existing systems that simply rely on historical resource utilization are not API-aware and thus cannot estimate the resource requirement accurately. This paper presents DeepRest, a deep learning-driven resource estimation system. DeepRest formulates resource estimation as a function of API traffic and learns the causality between user interactions and resource utilization directly in a production environment. Our evaluation shows that DeepRest can estimate resource requirements with over 90% accuracy, even if the API traffic to be estimated has never been observed (e.g., 3× more users than ever or unseen traffic shape). We further apply resource estimation for application sanity checks. DeepRest identifies system anomalies by verifying whether the resource utilization is justifiable by how the application is being used. It can successfully identify two major cyber threats: ransomware and cryptojacking attacks.