But manager Brad Ausmus said Detroit has given no thought at replacing Rodriguez at closer.
"We haven't had any discussions about any closing any one else other than Frankie," Ausmus said. "Until we decide otherwise, he's going to be our closer."
Rodriguez made quick work of the first two batters, striking out Yonder Alonso -- who belted a pair of home runs earlier in the contest -- and getting a line out from Ryon Healy. But after issuing a walk to A's backup catcher Bruce Maxwell, Rodriguez gave up a double to Matt Joyce and Rosales' game-winner on consecutive pitches.
"Any time you lose a game in the ninth inning, it stings," Ausmus said. "But it happens to every team, usually multiple times over the course of a season, and it happened tonight."
Rosales' hit snapped a streak of 14 1/3 scoreless innings by the Tigers' bullpen over five-plus contests.
After being charged with two earned runs in 2/3 innings of work, Rodriguez's ERA jumped to 6.35 on the year. Rodriguez racked up 44 saves and posted a 3.24 ERA in 61 appearances for Detroit last year, his first with the organization. Ausmus said Rodriguez just needs to work through some command issues.
"It's just the control, I think," Ausmus said. "He's having trouble commanding both his changeup and his fastball."
The Tigers had opportunities to put more runs on the board early, but ended up stranding 13 runners on the night. Detroit left the bases loaded in the first and fourth innings, as starter Jordan Zimmermann allowed four earned runs over 5 2/3 innings.
"We had some guys on base that we weren't able to push across," Ausmus said. "You're not going to score seven or eight runs every night. We had a lead with one out to go, we just didn't close it out."
Alex Espinoza is a contributor to MLB.com based out of the Bay Area, and covered the Tigers on Saturday. This story was not subject to the approval of Major League Baseball or its clubs.