We analyse the optical morphologies of galaxies in the IllustrisTNG simulation at z ̃ 0 with a convolutional neural network trained on visual morphologies in the Sloan Digital Sky Survey. We generate mock SDSS images of a mass complete sample of ̃ 12 000 galaxies in the simulation using the radiative transfer code SKIRT and include PSF and noise to match the SDSS r-band properties. The images are then processed through the exact same neural network used to estimate SDSS morphologies to classify simulated galaxies in four morphological classes (E, S0/a, Sab, Scd). The CNN model classifies simulated galaxies in one of the four main classes with the same uncertainty as for observed galaxies. The mass-size relations of the simulated galaxies divided by morphological type also reproduce well the slope and the normalization of observed relations which confirms a reasonable diversity of optical morphologies in the TNG suite. However we find a weak correlation between optical morphology and Sersic index in the TNG suite as opposed to SDSS which might require further investigation. The stellar mass functions (SMFs) decomposed into different morphologies still show some discrepancies with observations especially at the high-mass end. We find an overabundance of late-type galaxies (̃ 50{{ per cent}} versus ̃ 20{{ per cent}}) at the high-mass end [log(M*/M☉) > 11] of the SMF as compared to observations according to the CNN classifications and a lack of S0 galaxies (̃ 20{{ per cent}} versus ̃ 40{{ per cent}}) at intermediate masses. This work highlights the importance of detailed comparisons between observations and simulations in comparable conditions.