The larger impact of Jesse Owens was actually pretty much nill. What did happen however was that a split between the Nazi leadership and the German people was shown. The Nazi ideology held that the Germans were the so called Übermenschen, oder Master Race, and thus they should preform better than everyone else. The fact that a black man preformed well did not sit well with Hitler. Albert Speer, Hitler's Architect,Friend, and Armaments minister wrote this in his memoirs " "was highly annoyed by the series of triumphs by the marvelous colored American runner, Jesse Owens. People whose antecedents came from the jungle were primitive, Hitler said with a shrug; their physiques were stronger than those of civilized whites and hence should be excluded from future games. " ^1 . Hitler did not want to shake the hands of any black athletes, but did end up shaking Owens hand. Ruth Owens ( his wife ) said that after the event, the German crowds cheered him as they did any other athlete. He in some sense shattered the Nazi propaganda that only Aryans could be good, and all reports claimed that Hitler was incredibly annoyed.

So long term effects? Nothing really changed, but for the moment it was a huge shock to the NSPAD propaganda machine. Hope that helps.

Sources:

^1 Anspach, Emma; Almog, Hilah (2009). "Hitler, Nazi Philosophy and Sport". Duke.edu. Retrieved March 23, 2014.

Rick Shenkman, Adolf Hitler, Jesse Owens and the Olympics Myth of 1936 February 13, 2002 from History News Network (article excerpted from Rick Shenkman's Legends, Lies and Cherished Myths of American History, William Morrow & Co, 1988 ISBN 0-688-06580-5)

edited: cited my sources