Rosenthal has struggled of late, giving up at least two runs in three of his past five appearances.
"We just need to figure out a way to get him right and figure out how to get him to the point of being the pitcher he has been the last few years," Matheny said. "Right now, the ninth inning is a tough ask to do that. He will have a different role."
The Cardinals will use a three-pitcher committee to close games starting Saturday against the Seattle Mariners.
On Friday night, Rosenthal failed to retire any of the three batters he faced in the ninth inning of the Cardinals' 4-3 loss to the Mariners.
"I thought I was making some good pitches and it just kind of happened. It's not fun doing that, but I felt like I had good stuff. I made a pitch under the zone, but he [Adam Lind] just did a great job with it," Rosenthal said after allowing his third home run of the season.
Rosenthal, who got the closer's job in St. Louis in late 2013, led the majors with 93 total saves during the 2014 and 2015 seasons.