"I would never want to make it just about two players," McIlroy told reporters.
"I think that's a little disrespectful of all the other players that are trying to play well and trying to win tournaments."
World number one Koepka made worldwide headlines at the CJ Cup in South Korea last week after taking a swipe at the notion of a burgeoning rivalry with second-ranked McIlroy.
The American told AFP in an exclusive interview: "I've been out here for, what, five years. Rory hasn't won a major since I've been on the PGA Tour. So I just don't view it as a rivalry."
McIlroy initially responded on TV during Monday's exhibition match at Narashino Country Club, venue for this week's Zozo Championship in Japan.
"What Brooks said wasn't wrong," he said, adding, "I don't think he had to remind me I hadn't won one (a major) in a while, but you know."
Two days later the Northern Irishman was more thoughtful before he spoke.
"You look at what Justin Thomas has done over the last few weeks, you look at all the great players that are involved in golf and I think to make it just about two people is, you know, not the right thing to do or the right thing to say," he said.
The top two in the world rankings have distanced themselves from their peers in 2019.
Each won three times and Koepka retained his US PGA Championship while McIlroy became only the second player after Tiger Woods to win multiple Fedex Cups.
"I mean, I think any storyline where it's competitive at the top is going to be good for golf," said McIlroy.
"It doesn't have to be between me and Brooks, it could be between Justin Thomas and Dustin Johnson.
"You know, it could be between anyone. I think when it is competitive at the top and guys are jostling for that top position, I think that's a great thing for the sport. It gets people talking about it, it gets interest levels up."
McIlroy said there were a number of players who on current form could claim to be the best in the world, and there wasn't a lot to choose between them.
"I think for it just to be made about two people when parity in golf is something that is a real thing right now," he said.
"Five people could put their hand up and say they're the best player in the world right now."