Weak lensing by large-scale structure is a powerful technique to probe the dark components of the universe. To understand the measurement process of weak lensing and the associated systematic effects, image simulations are becoming increasingly important. For this purpose we present a first implementation of the $textit{Monte Carlo Control Loops}$ ($textit{MCCL}$; Refregier & Amara 2014), a coherent framework for studying systematic effects in weak lensing. It allows us to model and calibrate the shear measurement process using image simulations from the Ultra Fast Image Generator (UFig; Berge et al. 2013). We apply this framework to a subset of the data taken during the Science Verification period (SV) of the Dark Energy Survey (DES). We calibrate the UFig simulations to be statistically consistent with DES images. We then perform tolerance analyses by perturbing the simulation parameters and study their impact on the shear measurement at the one-point level. This allows us to determine the relative importance of different input parameters to the simulations. For spatially constant systematic errors and six simulation parameters, the calibration of the simulation reaches the weak lensing precision needed for the DES SV survey area. Furthermore, we find a sensitivity of the shear measurement to the intrinsic ellipticity distribution, and an interplay between the magnitude-size and the pixel value diagnostics in constraining the noise model. This work is the first application of the $textit{MCCL}$ framework to data and shows how it can be used to methodically study the impact of systematics on the cosmic shear measurement.