In a statement issued Saturday, Krzyzewski said "it is not my place to talk to another team's player" and he hoped he "did not create a distraction" for the top-seeded Ducks.
Oregon plays second-seeded Oklahoma in the regional final on Saturday afternoon.
Brooks made a three-pointer with the shot clock expiring in the final seconds of the Ducks' victory. In the handshake line, Krzyzewski had a prolonged discussion with the Oregon guard.
Krzyzewski said in his statement that chat "took the focus away from the terrific game that Dillon played."
The Hall of Fame coach also apologized for responding "incorrectly to a reporter's question about my comment to Dillon."
Brooks said in the locker room after the game that Krzyzewski told him that "I'm too good of a player to be showing (off) at the end."
In his news conference, Krzyzewski disputed Brooks' version of events and appeared angry when it was brought up.
"I didn't say that," Krzyzewski said. "You can say whatever you want. Dillon Brooks is a hell of a player. I said, `You're a terrific player.' And you can take whatever he said and go with it, all right?"
Here is Krzyzewski's statement in its entirety:
"Today, I spoke with Oregon head coach Dana Altman and apologized to him for my remarks to Dillon Brooks following our game. It is not my place to talk to another team's player and doing so took the focus away from the terrific game that Dillon played. In the postgame press conference, I reacted incorrectly to a reporter's question about my comment to Dillon. Clearly, the story that night was about Oregon advancing to the Elite Eight, and the outstanding game they played. I sincerely hope I did not create a distraction for Coach Altman and his team at this critical time of year. Certainly, I have the utmost respect for the Oregon program and their tremendous accomplishments."
Associated Press and Internet reports contributed to this story.
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