The functional magnetic properties of nanostructured materials can be distinctly different from their bulk counterparts. Understanding these properties is crucial for basic material science and for applications using nanostructured magnetic materials. However, determining intrinsic magnetic structures, exchange constants and local magnetic anisotropy in nanoparticles poses considerable challenges. Here, polarised neutron powder diffraction (PNPD) data, analysed in the frame of the Local Susceptibility and Model Hamiltonian approaches, is used to gain information on the contribution of the different magnetic sublattices on the magnetisation process in Mn3O4 nanoparticles in unprecedented detail. The magnetic order is found to be a Yafet-Kittel-type canted structure with inter- and intra-sublattice antiferromagnetic couplings, similar to bulk. PNPD corroborates that the c-axis is the hard-axis and the individual contributions of each magnetic site to the easy-plane magnetic anisotropy are determined. Remarkably, the analysis of the PNPD data provides the foremost determination of the microscopic magnetic parameters in nanoparticles, namely, intra- and inter- sub-lattice exchange constants and the local anisotropy parameter. The obtained values are consistent with bulk Mn3O4 experimental and theoretical results. These results open the path for the use of PNPD to gain unique magnetic information in nanostructured materials, particularly in complex, novel, or poorly understood systems.