The magnetic properties of individual Fe and Co atoms as well as of small Fe clusters adsorbed on two atomic layers of Al2O3 grown on Ni3Al(111) have been investigated by x-ray absorption spectroscopy and x-ray magnetic circular dichroism. We find ratios of the orbital over the effective spin magnetic moments of r=0.53 +/- 0.09 for Fe and r=0.91 +/- 0.06 for Co, which are both very close to the free-atom values of r=0.5 and 1, respectively. The magnetization curves acquired at the Fe and Ni edges demonstrate a distinctly different magnetization reversal of the transition-metal nanostructures and the substrate excluding magnetic dipolar or exchange coupling through the alumina film. Our data reveal an out-of-plane easy magnetization axis for Fe and Co originating from the spatially anisotropic hybridization of the 3d states of the adatom, with the 2p states of the oxygen terminated Al2O3 surface. We conclude that the alumina film effectively decouples the magnetic adatoms from the underlying metal substrate while providing a crystal-field environment giving rise to high magnetic anisotropy.