Model calibration is a central task faced by financial services institutions. Accurate and fast calibration is typically ensured by hard-coding calibration routines individually for different models. Alternatively, Monte Carlo calibration can be applied to a wide range of models. Typically parameter optimization is performed using potentially noisy approximate gradient computations or exact gradients computed via adjoint algorithmic differentiation (AAD). In this paper we introduce Automatic Monte Carlo Calibration (AMCC), which formulates Monte Carlo calibration as a deep learning problem. This point of view allows to easily apply backpropagation and gradient-based optimization schemes developed for deep learning to financial model calibration, bridging AAD and deep learning approaches. We showcase the flexibility of AMCC by calibrating a rough stochastic volatility model to options data.