The development of algorithms for automation of subtasks during robotic surgery can be accelerated by the availability of realistic simulation environments. In this work, we focus on one aspect of the realism of a surgical simulator, which is the positional accuracy of the robot. In current simulators, robots have perfect or near-perfect accuracy, which is not representative of their physical counterparts. We therefore propose a pair of neural networks, trained by data collected from a physical robot, to estimate both the controller error and the kinematic and non-kinematic error. These error estimates are then injected within the simulator to produce a simulated robot that has the characteristic performance of the physical robot. In this scenario, we believe it is sufficient for the estimated error used in the simulation to have a statistically similar distribution to the actual error of the physical robot. This is less stringent, and therefore more tenable, than the requirement for error compensation of a physical robot, where the estimated error should equal the actual error. Our results demonstrate that error injection reduces the mean position and orientation differences between the simulated and physical robots from 5.0 mm / 3.6 deg to 1.3 mm / 1.7 deg, respectively, which represents reductions by factors of 3.8 and 2.1.