According to the author himself, Sammy's "gesture of quitting has to do with the fact that she [Queenie] was rich and he was poor, as he sees it." For, Sammy's class awareness and his act of chivalry cannot bridge the "epochal gap."
In all his judgments of those who enter the grocery store, Sammy evaluates these people in terms of class. For instance, he calls the middle-aged women "a few houseslaves in pin curlers" and "sheep." But, when the young, pretty girls enter the grocery store, they appear to be superior in quality to the women with varicose veins, and Sammy yearns to gain their attention and do something for them. As they move about in the store, Sammy cannot take his eyes off the girls, especially the one he calls "Queenie." Clearly, his descriptions indicate his perspective of class differences between him and Queenie as he describes her speech and envisions her father and others in a white tuxedo jacket and the women "eating herring snacks on toothpicks."
In his act of Romantic independence, Sammy unties his apron, pulling it off his shoulders, ignoring Lengel's advice that he does "not want to do this." Unfortunately, Sammy's chivalrous act gains for him nothing as the girls leave and Sammy finds himself unaffected by any social elevation. So, Sammy finds himself sickened by "how hard the world was going to be ...hereafter" as he is now unemployed and among an even lower class than he was.