Feliciano is on the disabled list with a left rotator cuff strain and has not pitched in a game since March 9.
Feliciano is scheduled to resume playing catch on Wednesday, and Cashman said he believes Feliciano could make his Yankees debut in late April or early May.
"He was abused," Cashman said. "The concern is based on the MRI. The use pattern was abusive, but the MRI itself obviously shows what he's got. That leads us to believe this is resolvable and not a major issue."
Feliciano has led the Majors in relief outings in each of the last three seasons, setting a Major League record with 266 appearances over the three-season stretch.
The 34-year-old left-hander said his shoulder feels "weak," but it is improving and he is having his strength checked daily by doctors. He also said that the Mets were not to blame for his being on the disabled list to start this season.
Mets pitching coach Dan Warthen defended Feliciano's workload, saying the left-hander only wanted to help his former team.
"I feel badly that someone feels that way," Warthen said of Cashman's comments. "That was part of the reason we decided to not re-sign him -- because we knew we had used him 270-some times in the last three years.
"They didn't know that when they signed him? He volunteered for the baseball every day. He was asked whether he was able to pitch. He said, 'Yes' every day -- every day -- and wanted to pitch more than we even pitched him."
Cashman gave Feliciano a two-year, $8 million deal to switch boroughs as a situational lefty and said that the free-agent market forced him to cross his fingers and hope Feliciano would be healthy.
"It's a thin market when you're out there looking for lefties, and he's obviously one of the better ones out there," Cashman said. "You don't typically run to sign up guys that have been used like that."