Referring to Perez's form, Marko alluded to his "South American" heritage when comparing him to Max Verstappen and Sebastian Vettel, suggesting that he wasn't as focused as the team's two world champions.
"He is South American and he is just not as completely focused in his head as Max is or as Sebastian," Marko said.
The comments caused a stir on social media, especially in Perez's native Mexico, which is in North America.
Marko had already issued a public apology for the words he spoke on Red Bull's own ServusTV channel after the Italian GP, but Perez said ahead of the Singapore GP that they had also met in private.
"I had a private conversation with him," Perez said. "He did apologise. And that to me was the main thing.
"And yeah, basically, we move on. I have a personal relationship with him. And I think you can always have those feelings when you see that sort of stuff.
"Knowing the person helps a lot, because I know he doesn't mean it that way. And I took his apology, because I know Helmut from the personal relationship that we have that he doesn't mean it that way."
Perez insisted that he wasn't offended by Marko's comments, suggesting they had been misinterpreted.
"Not at all, if I'm totally honest," he said. "Knowing Helmut, like I say, have a personal relationship with him. I know, he doesn't mean it that way.
"I didn't get offended at all personally. Let's say if those comments were from a different perspective or so on, I would have to take them differently.
"But to me, it's just how things are, and I didn't take them personally."
He added: "Whatever I say to the media, or he says to the media, is different to the conversations we have. So anyway, we have a good relationship and I know that is not related to that side.
"Like I say, Helmut I did apologise, I think we all make mistakes. And what to me was the most important [thing] is that I take his apology, his personal apology.
"What happens afterwards, and on the media side or in public, that's not in my control. To me, the most important is the personal relationship.
"We will always have a chat on-track, off-track, here and there. We see each other pretty much every weekend.
"He will tell you what he thinks. I think something that we can appreciate from Helmut is that he is very transparent, to the media and to the world in general, and also to the drivers. So it's just how he is."
