The loss of tzaddikim has an effect on the world. "Save, O Lord - for the pious are gone; for the faithful have vanished from among men" (Psalms 12,2). That is to say, when a righteous man passes away, the world suffers a loss of emuna and trust. Emuna diminishes because tzaddikim help ensure that it remains strong, and when they leave, it becomes weaker. Rav Tzvi Yehuda was a great man of emuna, and his loss left a great vacuum of emuna in the world.