"I don't believe I'll ever get credit for anything I do in foreign affairs, no matter how successful it is, because I didn't go to Harvard"

Lyndon B. Johnson is expressing his disappointment with the reality that he thinks his successes in foreign affairs will not be recognized or credited due to the fact that he did not attend Harvard. This might recommend that he feels there is a particular level of elitism and favoritism towards Ivy League finishes in politics and society as a whole.