Several studies in mindfulness and meditation research have used the Attentional Network Task (ANT) to assess changes in the efficiency of attentional networks. The approaches used for mental training, the experimental designs, and the results in such studies are however heterogeneous, and in most cases, do not involve an assessment of dispositional mindfulness in its different facets. In this article, we originally report a study in which performances in the Attention Network Test Interactions (ANTI), a revised version of the ANT, are predicted by dispositional mindfulness facets (assessed through the five facets mindfulness questionnaire) in a population naïve to meditation. Regression analyses revealed that the mindfulness facets observe and acting with awareness were effective predictors of the efficiency of the three assessed attentional networks. Specifically, we found that observe scores predicted higher alerting scores. We also found that a higher acting with awareness score predicted slower response times when the executive control system was involved. Our results thus appear to contrast with other studies finding faster response times with mindfulness meditation training. More generally, our findings suggest that a higher dispositional mindfulness does not necessarily implicate an increased attentional efficiency in terms of response times.