Supported catalysts include an inorganic solid support such as silica that is functionalized to have inorganic acid functional groups attached thereto. The functionalization of the support material is optimized by (i) limiting the amount of water present during the functionalization reaction, (ii) using a concentrated mineral acid or derivative thereof, and/or (iii) increasing the reaction temperature and/or reaction pressure. The acid-functionalized support material serves as a support for a metal nanoparticle catalyst. The nanocatalyst particles are preferably bonded to the support material through an organic molecule, oligomer, or polymer having functional groups that can bind to both the nanocatalyst particles and to the support material. The supported catalysts can advantageously be used for the direct synthesis of hydrogen peroxide from hydrogen and oxygen feed streams.