Johnson said after the race that Newman raced him too hard for a car more than a lap down, allowing Greg Biffle to overtake him for the lead and eventual win.
He said the two discussed the issue this past week, but nothing was resolved.
"I appreciate his willing to talk to me and trying to clear the air,'' the five-time Sprint Cup champion said on Friday at Kansas Speedway. "I don't necessarily agree with (his explanation for why he drove that way). I'll let him explain that to you. I feel it's his right to say that.''
A Stewart-Haas Racing spokesperson said Newman was unavailable for comment.
Johnson acknowledged that Newman has a reputation for racing everyone hard, and went out of his way to make it clear he is not against racing hard.
But he was adamant there is a time and place for it, and that was not the time.
"That's one thing I have to be very careful about, because I love to race hard. That's not what it's about,'' Johnson said. "There's a time and a place. Two laps down, going your second lap down, with 20 laps to go, is not the right time.
"That's my point. At the end of a race, racing for any position, that's what we're here to do. I am not against that. There's a flow on the track that I think needs to take place, and it's been lost a little bit the last few years here. Again, I want to be careful. We're here to race. So I don't want to accuse someone of racing too hard. But in that situation at Texas, it just wasn't necessary."
For Johnson, it's all about respect. He said after the race there were "guys that were multiple laps down and didn't show much respect'' as he tried to hold a three-second lead over Biffle. He called out Newman specifically.
"Regardless of who it is, and I guess I think of the way I race, with 20 to go, even if I'm going down a lap I'm getting the hell out of the way,'' Johnson said. "Two laps down, I'm sure as hell getting out of the way.''
Johnson said there was a "general code 10 years ago'' that drivers gave each other that respect.
"Now it's really more of a general relationship that you have with guys,'' he said. "I know if I am 12 lengths from Tony (Stewart) and I run him down, I need to be ready for him to jump out of the gas. I've almost run him over ... because he gives that spot up.
"When the roles are reversed, I give him that same respect back. You don't get that from everybody. But being aware of what's going on at the end of the race is key. Who wants to be that guy at the end that affects the outcome?''