We carry out an accurate computational analysis on the nature and distribution of electronic trap states in shape-tailored anatase TiO2 structures, investigating the effect of the morphology on the electronic structure. Linear nanocrystal models up to 6 nm in length with various morphologies, reproducing both flattened and elongated rod-shaped TiO2 nanocrystals, have been investigated by DFT calculations, to clarify the effect of the crystal facet percentage on the nanocrystal electronic structure, with particular reference to the energetics and distribution of trap states. The calculated densities of states below the conduction band edge have been very well fitted assuming an exponential distribution of energies and have been correlated with experimental capacitance data. In good agreement with the experimental phenomenology our calculations show that elongated rod-shaped nanocrystals with higher values of the ratio between (100) and (101) facets exhibit a relatively deeper distribution of trap states. Our results point at the crucial role of the nanocrystal morphology on the trap state density, highlighting the importance of a balance between the low-energy (101) and high-energy (100)/(001) surface facets in individual TiO2 nanocrystals.