Over millions of years, nature has created complex hierarchical structures with exceptional mechanical properties. The nacre of various seashells is an example of such structures, which is formed out of a mainly inorganic mineral with organic material inclusions in a layered arrangement. Due to its high impact-resisting mechanical properties, these structures have been widely investigated and mimicked in artificial nacre-type composite materials. The artificial creation of nacre analogues for future applications requires an accurate understanding of their mechanical properties on the length scale of the nanoscale composite components. Here, we present an in-depth AFM study of the mechanical properties of Pāua nacre (Haliotis iris, 'rainbow abalone') and quantify the elastic modulus as well as related energy scales of both its main nanoscale constituents. We use AFM-based nano-indentation compared to standard micro/nano-indentation, which enables the direct determination of the mechanical properties of the biopolymer layer in nacre, including plastic and elastic energies during indentation. By combining three different AFM-based mechanical characterization methods we affirm the quantitativeness of our mechanical measurements and show that the organic layers have about half the elastic modulus of the inorganic aragonite regions. The obtained results reveal the detailed mechanical properties of the hierarchical structure of nacre and provide a strategy for accurately testing nanoscale mechanical properties of advanced composite materials.