  We show that an inequality, proven by K\"uronya-Pintye, which governs the
behavior of the log-canonical threshold of an ideal over $\mathbb{P}^n$ and
that of its Castelnuovo-Mumford regularity, can be applied to the setting of
principally polarized abelian varieties by substituting the Castelnuovo-Mumford
regularity with $\Theta$-regularity of Pareschi-Popa.
