Perturbations of the air transport network have a tremendous impact on many sectors of activity. Therefore, a better understanding of its robustness to targeted attacks is essential. The literature reports numerous investigations at different levels (world, regional, airline) considering various targeted attack strategies. However, few works consider the mesoscopic organization of the network. To fill this gap, we rely on the component structure recently introduced in the network literature. Indeed, the world air transportation network possesses seven local components capturing the regional flights in localized areas. Its global component, distributed worldwide, capture the interregional routes. We investigate the impact of two influential attacks (Degree, Betweenness) on the world air transportation network at the regional and inter-regional levels. Results show that the seven regions are isolated one after the other from the world air transportation network. Additionally, although the Betweenness attack effectively splits the network, its impact on regional routes is less pronounced.