Perez -- sidelined since late April -- suffered a setback with his left shoulder.
"I don't think Raffy is going to be able to pitch for us for the rest of the season," Acta said.
Perez has been dealing with a shoulder problem (officially described by the Indians as a strained left lat muscle) since Spring Training. The lefty pitched eight games (3.52 ERA) for Cleveland in April before landing on the disabled list, where he has remained all season long.
Asked if Perez might be facing surgery, Acta deferred to Indians head athletic trainer Lonnie Soloff. The Indians announced later that Perez's latest injury is a recurrence of inflammation and soreness in his throwing shoulder, noting that there were no current plans for surgical intervention.
Perez, 30, also sprained his right ankle during a Minor League rehab appearance for Triple-A Columbus on Aug. 11. The lefty had five Minor League outings, but was never able to return to full strength for Cleveland.
As a result, the Indians labored to find reliable left-handed relief pitching throughout this trying season. The slew of setbacks for Perez, who has spent parts of seven seasons with Cleveland, undeniably hurt the Tribe.
"It certainly didn't help us," Acta said. "He's been so reliable here for the last three years, the amount of appearances he piles up, and his ability to get lefties and righties at a certain part of the game. He can pitch in the sixth. He can pitch in the seventh or eighth, if you have to.
"Just being able to have that steady veteran guy out of the 'pen, we did kind of scuffle a little bit without him. We missed him."