Yes, the mighty predator sometimes sheds a tear. But not out of sadness or pity. Rather, this is a purely physiological Process. When the upper jaw is raised during feeding, it presses on a gland behind the eyelid, which then secretes a secretion. It is similar with the lachrymal fluid in humans, which forms when you press lightly on the inner corner of your eye. This is where the expression "pressing on the lacrimal gland" comes from.
The secretion from the eyes of crocodiles was considered mean and hypocritical. The phrase "crying crocodile tears" is therefore used when someone pretends to be sorry for something. The Liquid production is important for the preservation of the Eye Health in humans as well as in all vertebrates. However, humans are the only known species that cry for emotional reasons. Be it real or just a crocodile tear.