There are currently two well-accepted models that explain how pulsars exhibit glitches, sudden changes in their regular rotational spin-down. According to the starquake model, the glitch healing parameter, Q, which is measurable in some cases from pulsar timing, should be equal to the ratio of the moment of inertia of the superfluid core of a neutron star (NS) to its total moment of inertia. Measured values of the healing parameter from pulsar glitches can therefore be used in combination with realistic NS structure models as one test of the feasibility of the starquake model as a glitch mechanism. We have constructed NS models using seven representative equations of state of superdense matter to test whether starquakes can account for glitches observed in the Crab and Vela pulsars, for which the most extensive and accurate glitch data are available. We also present a compilation of all measured values of Q for Crab and Vela glitches to date which have been separately published in the literature. We have computed the fractional core moment of inertia for stellar models covering a range of NS masses and find that for stable NSs in the realistic mass range 1.4 +/- 0.2 solar masses, the fraction is greater than 0.55 in all cases. This range is not consistent with the observational restriction Q < 0.2 for Vela if starquakes are the cause of its glitches. This confirms results of previous studies of the Vela pulsar which have suggested that starquakes are not a feasible mechanism for Vela glitches. The much larger values of Q observed for Crab glitches (Q > 0.7) are consistent with the starquake model predictions and support previous conclusions that starquakes can be the cause of Crab glitches.