The incident occurred in the third quarter of the match when Livingston reached between Nowitzki's legs and struck him in the groin.
Livingston served his suspension during Golden State's 107-92 loss to the San Antonio Spurs at the AT&T Center on Sunday night.
However, Livingston claims that he did not intend to deliver a low blow to the 7-footer.
"He kind of sat back to create space with his lower area, and it was just bad timing," Livingston said after the game. "Eleven years in the league, I haven't had a dirty play. I haven't made a name in this league by playing that way. It looked worse than it actually was.
"It's Dirk Nowitzki. It's a Hall of Fame player. You don't do that to somebody like that."
Nowitzki gave Livingston "the benefit of the doubt" since the 29-year-old is not known for being a dirty player.
"Well, I give him the benefit of the doubt because he's really not that type of player," Nowitzki said. "He hasn't been his entire career. I'm not really sure what he was trying to do there, if he was trying to get to the ball through my legs or anything.
"But like I said, he's not a dirty player. He's actually a really, really good dude, so I'll give him the benefit of the doubt."