We apply the random matrix theory to the study of quasi-localized modes in amorphous solids having correlated disorder due to the stability criterion. We demonstrate that the number and properties of quasi-local vibrations depend  significantly on how much the statistics of the dynamical matrix elements differs from the Gaussian one. The quasi-localized regime of the vibrational density of states can be understood in the framework of a perturbation theory,  which managed to identify the low-frequency asymptotic.