There were two graphs, one for incidence and one for mortality. The rate of mortality had been decreasing long before measles vaccination.
As for incidence of measles, show me a graph that accounts for the increase of fifty million people in the U.S. population between 1945 and 1963. Then, if that doesn't show a downward trend, we can discuss the historical correlation between measles incidence and economic boom and bust cycles or the fact that people were intentionally getting measles infections to gain life-long immunity. You don't know what the situation would look like if people used common sense, evidence-based preventative measures like quarantine. As I've pointed out several times, people back then considered measles a mild, harmless infection, else they wouldn't have taken their kids to measles parties.