Auerbach, who turned 89 last week, died Saturday of an apparent heart attack near his home in Washington, D.C.
"I knew Red very well," Layden said. "I knew he wasn't well. I knew he was having some health problems. I'm sorry to hear he has passed, although 89, that's a pretty good ticket."
Auerbach coached the Boston Celtics to nine NBA championships, including eight in a row from 1959 to 1966. After he moved to the front office, the Celtics won seven more titles.
Jazz vice president of basketball operations Kevin O'Connor remembers Auerbach for those dynasty years.
"He deserves an awful lot of credit," O'Connor said, "because he didn't have just one great team. He had two. . . . He turned that team over and still won. That's a difficult thing to do."
According to O'Connor, Auerbach was "ahead of his time in terms of scouting and finding players. And not only was he wonderful at picking out talent, but he was a terrific coach."
Like Layden, Auerbach was born in Brooklyn.
"We're going to miss him," Layden said. "He was a figure to be reckoned with. He went through the hard times and the great times [of the NBA]. He was a very intelligent guy - very shrewd but very honest.
"I'm sorry to hear he passed, but it was a privilege knowing him. I put knowing Red next to knowing Johnny Wooden. And Red Holzman. Just special people. All of them."
Auerbach and Layden were central figures in one deal that impacted both franchises.
In 1980, Boston owned the No. 1 draft pick, Utah owned the No. 2 pick and Golden State owned the No. 3 pick.
Auerbach knew the Warriors wanted Purdue center Joe Barry Carroll and he wanted to make a trade with them.
The day before the draft, Auberbach called Layden, wanting to know if the Jazz planned to take Louisville's Darrell Griffith or Minnesota's Kevin McHale.
"He said, 'Look, it would be better for both of us if we each knew what they other was going to do,' " Layden recalled. "He said, 'If you take McHale, we'll take Griffith.' I said, 'We're going to take Griffith. We really need a marquee name.' "
The next day, Boston traded the No. 1 pick to Golden State, which selected Carroll. The Jazz took Griffith, the reigning collegiate player of the year. Boston, which also got center Robert Parish in the deal, grabbed McHale.
"The next day Red called me," Layden said. "He said, 'Rook, anytime you can take a center, take a center. I like Griffith and would have taken him. But mark my word: McHale is going to be something special.' "
Griffith enjoyed a productive career in Utah - "He was pretty special for us, too," Layden insists - but McHale became a perennial All-Star and Hall of Famer.
Layden also recalled how he would battle to sit next to Auerbach when they were attending the same function.
"Just to hear what the guy would say," he explained.
Once, Layden asked Auerbach to autograph a picture of the two men shaking hands.
When Auerbach declined, Layden said, " 'What do you mean?' And Red said, 'Not unless you sign one for me.' That's the kind of guy he was."