Directional detection is a promising search strategy to discover Galactic dark matter. Taking advantage on the rotation of the Solar System around the Galactic center through the dark matter halo, it allows us to show a direction dependence of weakly interacting massive particle (WIMP) events. Even though the goal of directional search is to identify a WIMP positive detection, exclusion limits are still needed for very low exposure with a rather large background contamination, such as the one obtained with prototype experiments. Data of directional detectors are composed of energy and a 3D track for all recoiling nuclei. However, to set robust exclusion limits, we focus on the angular part of the event distribution, arguing that the energy part of the background distribution is unknown. As the angular distributions of both background and WIMP events are known, a Bayesian approach to set exclusion limits is possible. In this paper, a new statistical method based on an extended likelihood is proposed, compared to existing ones, and is shown to be optimal. Eventually, a comprehensive study of the effect of a detector configuration on exclusion limits is presented. It includes the effect of having or not sense recognition, a finite angular resolution, taking into account energy threshold as well as some astrophysical uncertainties.