Cavs owner Don Gilbert promoted Griffin from interim general manager on Monday. He replaced Chris Grant, who was ousted as the team's GM in February.
"Any -- any -- insinuation that Kyrie Irving had anything to do with this decision is patently false," Griffin said, according to the Cleveland Plain Dealer. "It's unfair. He was not consulted on this decision, nor was he consulted on the previous decision. It's a completely unfair assertion and one that I want everyone to understand very clearly that is not a narrative we are going to go with."
Irving expressed his displeasure with the situation in Cleveland at times during the past season but denied rumors that he wants to go elsewhere when his contract expires after the 2014-15 season.
Griffin said there is no timetable to name a successor to Brown, who had four years left on a $20 million contract.
Alvin Gentry, Vinny Del Negro and Mike D'Antoni have emerged as early potential candidates to replace Brown, according to ESPN.com. Other possibilities include Mark Jackson and George Karl. Griffin also has worked with Steve Kerr, who is reported to be the front-runner for the New York Knicks' vacancy.
Brown lasted one season in his second stint with the Cavs, who finished with a 33-49 record and out of the playoffs for the fourth consecutive year. He previously was fired by the Los Angeles Lakers after serving as Cavs coach from 2005 to 2010.