Permanent grassland soils have high carbon sequestration potential, but this potential is highly dependent on environmental conditions and grazing practices. In this paper, we study the impact of herbivore grazing intensity on grassland carbon storage. We present and study a parsimonious stocks and fluxes model coupling carbon and nitrogen cycles and including microbial decomposers, root exudates, rhizosphere priming effect and the impact of grazing by domestic herbivores. Our main objective is to understand the mechanisms through which herbivore grazing can contribute to increasing carbon stocks in grasslands. Analysis of model outcomes shows that the bell-shaped response of carbon storage to grazing intensity, as reported in the literature, is the exception rather than the rule. The study also demonstrates that net primary production alone is not a reliable indicator of carbon sequestration. While increasing grazing intensity can lead to an increase in grassland carbon stocks at steady state, this only occurs if the increase in NPP is sufficient to compensate for the increase in carbon output by herbivores. Finally, the study identifies herbivore-induced root exudation as a potential yet underexplored mechanism that could be optimised to increase carbon storage. In this regard, it would be interesting to identify the management practices (timing, duration, intensity, and frequency of grazing) that optimize this mechanism.