The angst that is articulated in the poem can be seen when the cockroach tries to figure out where it should go and what should it do. The speaker notices this in the cockroach and sees it as a mirror to his own condition of being: "He looked uncertain where to go." From skittering about and making designs on the floor, the cockroach had ascended to a particular point and thus wondered where he should go. Puzzled in what to and where to go, possibly brought on by "due payment for some vicious crime," the speaker feels angst because in the condition of the insect, he "recognized" his own being in the world.
There is angst in seeing that the cockroach and the human being are no different than one another. Both struggle to find meaning in what they do and in who they are. They are both filled with action, but find their condition impotent in not knowing the path they are to follow. The speaker projects how sins from the past cast a shadow on the direction of the future and in the present. It is this state of being that causes angst in the human being, for he has been able to link his own condition to that of the insect.