Both clubs are still in the bottom three but Tomasso Rocchi's winner could go along way to deciding both clubs' fate.
Perotti said: "We had many difficulties in the first half because Perugia didn't allow us to play.
"In the second half Rocchi scored, then we defended for our lives because the win was so important."
Perugia boss Serse Cosmi refused to throw in the towel just yet even though time is running out.
"In football, what counts is numbers," said Cosmi.
"But I must think that we have what it takes to recover. Today we can't complain. We made mistakes in attack and one in defence.
"We will go back home beaten but not dead."
