Functional connectivity is commonly used for studying functional interactions among brain regions. However, its results are affected by noise and/or physiological artifacts, especially when computed using blood-oxygen-level-dependent (BOLD) functional magnetic resonance imaging (fMRI) signals. In this study, we assessed the effect of these artifacts by simulating physiological and BOLD fMRI signals during resting and task conditions and quantifying the resulting functional connectivity results patterns by well established methods (full and partial correlation). Our results reveal that the regions with similar physiological response functions were adversely affected by physiological artifacts. Notably, functional connectivity values computed during task execution exhibited lower errors compared to those computed during the rest period. Furthermore, the results computed using the partial correlation method consistently yielded lower errors compared to those computed using full correlation. Overall, our findings quantitatively characterize the impact of physiological artifacts on functional connectivity patterns and emphasize the importance of method choice in mitigating the impact of artifacts.