Mathematical models of induction motor (IM) used in direct field-oriented control (DFOC) strategies are characterized by parametrization resulting from the IM equivalent circuit and model-type selection. The parameter inaccuracy causes DFOC detuning, which deteriorates the drive performance. Therefore, many methods for parameter adaptation were developed in the literature. One class of algorithms, popular due to their simplicity, includes estimators based on the model reference adaptive system (MRAS). Their main disadvantage is the dependence on other machines’ parameters. However, although typically not considered in the respective literature, there are other aspects that impair the performance of the MRAS estimators. These include, but are not limited to, the nonlinear phenomenon of iron losses, the effect of necessary discretization of the algorithms and selection of the sampling time, and the influence of the supply inverter nonlinear behavior. Therefore, this paper aims to study the effect of the above-mentioned negative aspects on the performance of selected MRAS estimators: active and reactive power MRAS for the stator and rotor resistance estimation. Furthermore, improved reduced-order models and MRAS estimators that consider the iron loss phenomenon are also presented to examine the iron loss influence. Another merit of this paper is that it shows clearly and in one place how DFOC, with the included effect of iron losses and inverter nonlinearities, can be modeled using simulation tools. The modeling of the IM and DFOC takes place in MATLAB/Simulink environment.