By all means, tell your professor why the assignment was late. Your professor may interpret your silence as a sign that you either don't care that your work is late or that you have no reason to explain your lateness. Most teachers, even if they have a lenient policy on late assignments, expect assignments to be turned in on the due date, and if your assignment is late, your professor may interpret the lateness as a sign of disrespect, which, in many circumstances, it is.
If you have an acceptable reason for your lateness, your professor will at least see your explanation as a polite attempt to justify yourself. If you have no good reason, then couch your explanation in something like this: "Although I don't have a good excuse for turning my assignment in late, I do have a reason to explain my tardiness. . . ." And then briefly explain the cause of the lateness.
In almost all cases, more, rather than less, communication with your teachers is a good idea.