We investigate the effects that a phase transformation, from isotropic to orientationally (nematic) and positionally (smectic) ordered mesophases, has on the energy transfer process between solute molecules. We combine Metropolis Monte Carlo simulations and a master equation approach to study radiationless energy transfer processes in three-dimensional ordered systems of identical uniaxial particles interacting via the Gay-Berne potential. The time-dependent excitation probability and the fluorescence anisotropy decay curves show an enhanced energy transfer in systems with a higher degree of order. We also find a non-isotropic evolution of the time-dependent excitation probability in systems with positional as well as orientational order, with a faster energy transfer in the smectic planes.