We study the contribution of triplet exciton diffusion to the efficiency loss resulting from Förster-type triplet-triplet annihilation (TTA) in organic phosphorescent semiconductor host-guest systems, using kinetic Monte Carlo (KMC) simulations. Our study focusses on diffusion due to Förster-type guest-guest transfer, but includes also a comparison with simulation results for the case of Dexter-type guest-guest transfer. The simulations are carried out for a wide range of Förster radii, and for guest concentrations up to 100 mol%, with the purpose to support analyses of time-resolved photoluminescence experiments probing TTA. We find that the relative contribution of diffusion to the TTA-induced efficiency loss may be deduced quite accurately from a quantitative experimental measure for the shape of the time-dependent photoluminescence intensity, the so-called r ratio. For small guest concentrations and Förster radii that are most relevant to organic light-emitting diodes (OLEDs), the diffusion contribution is in general quite small. Under these weak-diffusion conditions, the absolute diffusion contribution to the TTA-induced efficiency loss can be understood quantitatively using a capture radius formalism. The effective guest-guest diffusion coefficient that follows from the TTA simulations, using the capture radius formalism, agrees well with the diffusion coefficient that follows from direct KMC diffusion simulations. The simulations reveal that the diffusion coefficient is strongly affected by the randomness of the distribution of guest molecule locations.