The security analysis of quantum key distribution is difficult to perform when there is efficiency mismatch between various threshold detectors involved in an experimental setup. Even the verification that the device actually performs in the quantum domain, referred to as the task of entanglement verification, is hard to perform. In this article we provide such an entanglement-verification method for characterized detection-efficiency mismatch. Our method does not rely on a cut-off of photon numbers in the optical signal. It can be applied independently of the degrees of freedom involved, thus covering, for example, efficiency mismatch in polarization and time-bin modes, but also in spatial modes. The evaluation of typical experimental scenarios suggests that an increase of detection-efficiency mismatch will drive the performance of a given setup out of the quantum domain.