The exchange bias properties of 5 nm Co/CoO ferromagnetic/antiferromagnetic core/shell nanoparticles, highly dispersed in a CuO matrix, have been optimized by matching the lattice parameter of the matrix with that of the CoO shell. Exchange bias and coercivity fields as large as H = 7780 Oe and H = 6950 Oe are linked to the presence of a CuO matrix (0.3% lattice mismatch with respect to the shells). The small mismatch between CuO and CoO plays a dual role: it (i) structurally stabilizes the CoO and (ii) favors the existence of a large amount of uncompensated moments in the shell that enhance the exchange bias effects. The results indicate that lattice matching may be a very efficient way to improve the exchange bias properties of core/shell nanoparticles, paving the way to novel approaches to tune their magnetic properties.