Biodiversity loss not only implies the loss of species but also entails losses in other dimensions of biodiversity, such as functional, phylogenetic and interaction diversity. Yet, each of those facets of biodiversity may respond differently to extinctions. Here, we examine how extinction, driven by climate and land‐use changes may affect those different facets of diversity by combining empirical data on anuran–prey interaction networks, species distribution modelling and extinction simulations in assemblages representing four Neotropical ecoregions. We found a mismatch in the response of functional, phylogenetic and interaction diversity to extinction. In spite of high network robustness to extinction, the effects on interaction diversity were stronger than those on phylogenetic and functional diversity, declining linearly with species loss. Although it is often assumed that interaction patterns are reflected by functional diversity, assessing species interactions may be necessary to understand how species loss translates into the loss of ecosystem functions.