Italy lost all five of their RBS 6 Nations matches but Parisse again led from the front throughout and as a result he is doubtful for Stade Francais' clash with Toulouse in the Top 14 this weekend.
And Quesada admitted he will not be rushing Parisse back into action, admitting the 30-year-old needs time to recover.
"We are going to wait until the last minute to decide because he is a very important player for the group," said Quesada.
"He had two, three niggles and he gave his all in the last match (against England in the RBS Nations last Saturday) but his health has suffered.
'He has passed the tests and is taking care of himself. We will put everything in place to help him recover but his chances are very low."