The duo addressed the incident for the first time Tuesday night after the Lakers' 107-100 win over the Memphis Grizzlies.
"The situation, like we said, was just a miscommunication between both sides," Clarkson said. "We don't want to go into further detail about who's right and who's wrong in that situation. But at the end of the day, it was a miscommunication."
Earlier Tuesday, Lakers spokesman John Black said in a statement that there were "different interpretations" of what occurred Sunday night.
The woman who made the allegation is Alexis Jones, an activist trying to stop athletes from committing sexual harassment, sexual abuse and domestic violence.
Jones told ESPN in an interview Monday that at about 7:30 p.m. Sunday she and her 68-year-old mother stopped their vehicle at a Hollywood intersection, where a Jeep with four men pulled up alongside them.
According to Jones, the men inside the Jeep began making "vulgar, sexual" gestures toward her mother. Jones took pictures of the men with her phone and posted them to Instagram, where commenters identified them as Young and Clarkson.
"We've looked into the situation and spoken to Alexis Jones as well as to Nick Young and Jordan Clarkson," Black said in the statement. "Based on these conversations, our conclusion is that there are different interpretations of what happened.
"We support Nick and Jordan and believe what they told us about the incidents and their actions. We also are supportive of Alexis and her feelings about what happened, about women's rights, and of the fine work Alexis is doing with her organization.
"I had several conversations with Alexis and her publicist, and tried to arrange a meeting between her, Nick and Jordan. Unfortunately, Alexis's schedule didn't allow for this to happen yesterday. We will also continue to stay in touch with her about the possibility of addressing our team about the important issues with which she's involved."
Coach Byron Scott also said he spoke with the players about the events of Sunday night.
"I talked to those guys [Monday] about that incident," Scott said Tuesday night before the Lakers faced the Grizzlies. "My conversation with them is always private, and we're just going to leave it at that."
Young said after Tuesday's game that he learned he has to watch his surroundings.
"We live in a world where social media plays a big part in what you do so you've just got to be careful about your surroundings and where you're at," he said.
Clarkson started Tuesday night and had a team-high 22 points in the Lakers' win. Young was expected to play but never entered the game.
The Lakers haven't indicated any intention of taking disciplinary action against Young or Clarkson.
The Associated Press contributed to this report.
Athletes more cognizant of how they treat women
Rachel Nichols, Brian Windhorst and Tracy McGrady share their thoughts on the Lakers looking into sexual harassment accusations involving Jordan Clarkson and Nick Young and discuss how these issues have evolved with the rise of social media.