The tone created is very similar to the ominous timbre evoked with the poem that inspired the title. If we examine the end of Achebe's work with Yeats' "The Second Coming," there are some distinct tonal similarities. Achebe's narrative displays how there is an inexorable descent into subjugation and violation that is going to be present for the Ibo people. Yeats' poem surveys the destroyed landscape of post World War I Europe and warns of a vision that is actually worse. The idea of "the center cannot hold" is present in both in Achebe's vision for Africa under colonial rule and a Europe that is struggling to find order in the midst of disorder. This idea of a fragmented social setting and the destruction of old world values is a similar tone in both the ending to Achebe's work and in Yeats' poem, as both works stress that the values to which individuals clung no longer apply in a new setting.
Of course, ostensibly, the tone created is one of finality, of things being finished and having run their natural course. One of the things about the ending of the book though, is that in some ways the end is just beginning, things are just beginning to really fall apart. This one village has seen its champion hang himself, but the really terrible clash between the cultures has just gotten its start, though it won't take long to perhaps run its course.
So in some ways, I would suggest that the use of the phrase is also suggestive, paradoxically, that things are not going to come to an end, that they will continue and knowing the story will perhaps help us to move in a better direction.