I'm not certain what type of answer you are looking for.
If you want the Star Trek Universe reason why, difference Between the Modern Day Klingons and the original series Klingons was untalked about, among Klingons. (Wharf a Modern day Klingon from TNG was asked the question, why do they look so different and he said, "I Don't want to talk about it.")
If you want the actual reason, because in the 60's, the shows producers/writers did not consider making the Klingons look so different from humans. The TNG and more recent shows Producers/Writers/Directors had more imagination.