Digital Breast Tomosynthesis (DBT) is an X-ray modality enabling to reconstruct 3D volumes in the context of breast cancer screening. However, because of the limited angle and sparse view constraints, artefacts emerge in the reconstructions and greatly reduce their quality. In a previous work, we proposed a post-processing deep learning reconstruction pipeline for DBT that is trained using synthetic data. Owing to the geometrical limitations of the acquisition device, the amount of information to extrapolate is important and the neural network could inevitably commit errors. As such, the reconstructed volumes are not completely reliable, and exact consistency with the measurements is not guaranteed. In this study, we first propose two methods to estimate the uncertainty of the model reconstructions, and show that the result can be used as a proxy of the true error. Secondly, we explore the minimisation of a data consistency term constrained by the predicted uncertainty, in order to mitigate the network errors. We demonstrate experimentally that this approach enhances the quality of reconstruction as compared to reintroducing projections information without constraint.