Rodriguez, 35, struggled for the Tigers this season, posting a 7.82 ERA in 28 games. In what would be his last appearance for the team Thursday night, he loaded the bases before giving up a grand slam to Robinson Cano. Detroit fell to the Mariners, 9-6, its sixth-consecutive loss.
Ausmus said Rodriguez handled the decision with class.
"He was as gracious and as professional as I would have expected,'' Ausmus said. "He had been that way, with the staff and his teammates, since he got here.
"He is a tremendous leader in the bullpen, but it just wasn't working on the field. And quite frankly the reason we stuck with him is he is a good leader, he is a good guy to have on the team and he is a positive influence.''
Rodriguez ranks fourth on the all-time saves list with 437.
In 2016, Rodriguez was effective as Detroit's closer, saving 44 games and posting a 3.24 ERA, but Ausmus handed closing duties to Justin Wilson earlier this year. In his amended relief role, Rodriguez wasn't able to make enough of an impression to win the position back, and was vocal about his diminished role.
Starter Justin Verlander was talking-up Rodriguez in one corner of the Tigers' clubhouse, confident that he'll resurface.
"He's got a great career behind him, but I didn't think he is done,'' Verlander said. "I think he's hit a bit of a rough patch and he's too good not to figure it out.''
Taking Rodriguez's place on the pitching staff is Bruce Rondon, who was sent to Triple-A Toledo in April after early-season struggles.
"We're going to find out,'' Ausmus said in what he expects from Rondon. "He struggled with his command when he was here earlier in the season and he struggled with it when he first got to Toledo. But by all accounts, he's pitched well lately. We need him to pitch well. It's as simple as that.''
The Tigers also moved outfielder Alex Presley to the seven-day concussion disabled list and, in a corresponding move, selected the contract of veteran outfielder Matt den Dekker from Toledo to fill Presley's roster spot.
"Moving around is not the best for me right now, is the best way to describe it,'' Presley said.
Jay Paris is a contributor to MLB.com based in San Diego. He covered the Tigers on Friday.