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We make use of z = 0 samples of strongly barred and unbarred disc galaxies from the TNG100 and TNG50 cosmological hydrodynamical simulations to assess the performance of the simple disc instability criterion proposed by Efstathiou, Lake & Negroponte (1982) (ELN-criterion). We find that strongly barred galaxies generally assemble earlier, are more star-dominated in their central regions, and have more massive and more compact discs than unbarred galaxies. The ELN-criterion successfully identifies ~75% and ~80% of the strongly barred and the unbarred galaxies, respectively. Strongly barred galaxies that the criterion fails to identify tend to have more extended discs, higher spin values and bars that assembled later than is typical for the bulk of the barred population. The bars in many of these cases appear to be produced by an interaction with a close neighbour (i.e. to be externally triggered) rather than to result from secular growth in the disc. On the other hand, we find that unbarred galaxies misclassified as barred by the ELN-criterion typically have stellar discs similar to those of barred galaxies, although more extended in the vertical direction and less star-dominated in their central regions, possibly reflecting later formation times. In addition, the bulge component of these galaxies is significantly more prominent at early times than in the strongly barred sample. Thus, the ELN-criterion robustly identifies secular bar instabilities in most simulated disc galaxies, but additional environmental criteria are needed to account for interaction-induced bar formation.