Data-driven control in unknown environments requires a clear understanding of the involved uncertainties for ensuring safety and efficient exploration. While aleatoric uncertainty that arises from measurement noise can often be explicitly modeled given a parametric description, it can be harder to model epistemic uncertainty, which describes the presence or absence of training data. The latter can be particularly useful for implementing exploratory control strategies when system dynamics are unknown. We propose a novel method for detecting the absence of training data using deep learning, which gives a continuous valued scalar output between $0$ (indicating low uncertainty) and $1$ (indicating high uncertainty). We utilize this detector as a proxy for epistemic uncertainty and show its advantages over existing approaches on synthetic and real-world datasets. Our approach can be directly combined with aleatoric uncertainty estimates and allows for uncertainty estimation in real-time as the inference is sample-free unlike existing approaches for uncertainty modeling. We further demonstrate the practicality of this uncertainty estimate in deploying online data-efficient control on a simulated quadcopter acted upon by an unknown disturbance model.