Resting-state brain activity, as observed via functional magnetic resonance imaging (fMRI), displays non-random fluctuations whose covariance structure (aka functional connectivity; FC) is commonly parsed into spatial patterns of positive and negative correlations (PCs and NCs). Mapping NC patterns for certain key seed regions has shown considerable promise in recent years as a tool for enhancing neuro-navigated targeting and clinical outcomes of repetitive transcranial magnetic stimulation (rTMS) therapies in psychiatry. These successes bring to the fore several major outstanding questions around the neurophysiological origins of fMRI NCs, the answers to which should prove useful for future therapeutic protocol development. In this work, we studied candidate mechanisms for the emergence of fMRI NCs using connectome-based computational modeling. Simulations of fMRI data under manipulation of inhibitory parameters WI and λ, representing local and network-mediated inhibition respectively, were explored, focusing on the impact of inhibition levels on the emergence of NCs. Despite the considerable difference in time scales between GABAergic neuronal inhibition (tens of ms) and fMRI FC (dozens of seconds), a clear relationship was observed, whereby the greater levels of overall inhibition led to significantly greater magnitude and spatial extent of NCs. We show that this effect is due to a leftward shift in the FC correlation distribution, leading to a reduction in the number of PCs and a concomitant increase in the number of NCs. Relatedly, we observed that those connections available for recruitment as NCs were precisely those with the weakest corresponding structural connectivity. Relative to nominally default values for the models used, greater levels of inhibition also improved, quantitatively and qualitatively, single-subject fits of simulated to empirical FC matrices. Our results provide new insights into how individual variability in anatomical connectivity strengths and neuronal inhibition levels may determine individualized expression of NCs in fMRI data. These, in turn, may offer new directions for optimization and personalization of rTMS therapies and other clinical applications of fMRI NC patterns.