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Global warming forces the automotive industry to reduce real driving emissions and thus, its CO2 footprint. Besides maximizing the individual efficiency of powertrain components, there is also energy-saving potential in the choice of driving strategy. Many research works have noted the potential of model predictive control (MPC) methods to reduce energy consumption. However, this results in a complex control system with many parameters that affect the energy efficiency. Thus, an important question remains: how do these partially uncertain (system or controller) parameters influence the energy efficiency? In this article, a global variance-based sensitivity analysis method is used to answer this question. Therefore, a detailed powertrain model controlled by a longitudinal nonlinear MPC (NMPC) is developed and parameterized. Afterwards, a qualitative Morris screening is performed on this model, in order to reduce the parameter set. Subsequently, the remaining parameters are quantified using Generalized Sobol Indices, in order to take the time dependence of physical processes into account. This analysis reveals that the variations in vehicle mass, battery temperature, rolling resistance and auxiliary consumers have the greatest influence on the energy consumption. In contrast, the parameters of the NMPC only account for a maximum of 5% of the output variance.