Militarily, while the Civil War is in some ways a prefigure of WWI, the comparison only usefully reaches so far. In particular, Civil War artillery lacked the absolute primacy achieved by later developments, permitting a much more mobile style of warfare and preventing the stasis observed on the Western Front. The Civil War's belligerents were also much more unevenly matched, making it possible for a single engagement to produce a decisive strategic outcome; no such possibility existed in WWI until much later in the war, when new technology came along to counter the primacy of artillery and break the stalemate of the trenches.
Politically speaking, too, we observe a qualitative postwar difference; harsh as the military occupation of the South was in many ways, and in spite of bastards like Butler, there existed a strong desire for conciliation and reintegration of the erstwhile secessionists, which overall found considerable success; while the cultural and economic differences underlying the war largely still exist to this day, we've just passed the sesquicentennial of Appomattox without at any point seeing a serious desire for, or risk of, a new outbreak of warfare. Versailles, by contrast, while no doubt seeming justified to its authors in the astonishingly punitive terms it imposed, produced a new and much uglier war within just a few decades.
So, no, I can't really agree with you here. It's accurate to say that the Civil War is by far the ugliest war whose effects our young nation has ever directly felt. It is not at all accurate to say that those effects are in any way comparable in severity to those of the First World War - which, indeed, was nothing like we've ever seen in America, a fact for which, should you be so inclined, I recommend you nightly thank God.