Dr. King And Denzel

(CBS)  As the nation celebrates the life, work and legacy of the late Dr. Martin Luther King Jr. on Monday, two-time Oscar-winning actor and director Denzel Washington reflected on how the civil rights leader's teachings affected, and continue to affect, his life, as well as what he's passing down to his own children.

On The Early Show Monday, co-anchor Harry Smith asked Washington whether Dr. King was "a part of the conversation" in his household.

"You know," Washington responded, "My father was a minister. So there was this talk of this other guy, Malcolm X, that was not allowed to somehow be talked about, and of course there was Martin Luther King.

"In retrospect, I think what he and Malcolm X and John Kennedy and Robert Kennedy had in common is they were the first television stars, if you will, leaders. Television activists, I mean. Of course, I remember the March on Washington, famous speech and things like that. You know, you had this image, (and) now this person's in your house."

Washington says he was shielded by his parents from some of the discrimination his family experienced.

"You know what was interesting for my generation," Washington remembered, "is that, because we were sort of protected, I remember taking trips down South - our father grew up in Virginia - and I remember us not being able to stop at places. I didn't quite know why. It was like, we hit the Jersey Turnpike, he gassed up. You went all the way to Virginia. You hit the last Howard Johnson's, and that was it, you know? Or they brought the food with us, you know? And I didn't exactly know why.

"But what I felt later on, as a young adult, because I had learned all this and had been drilled, and I'd been programmed by my parents and my mother and taught all of these things and seen some of these things, you thought, in your lifetime, 'Oh, everything's going to be perfect, like Martin Luther King said.' And then you get out there in the real world, and it ain't.

"I try to teach my children there are going to be obstacles. Someone may not like you just because they don't like themselves. You know what I mean? But don't you get bogged down, and don't be a hater, you know? Don't let hatred destroy you, you know? Overcome it. Move on. Educate them, if you will."

Asked if he thinks Dr. King's work is front of mind for today's young people, Washington said, "I think it is, more than we older people give younger people credit for."