The Italian guardian was taken off with a hamstring injury to be replaced by reserve keeper Hilario, as the Blues were already without first-choice Petr Cech.
Cech is ruled out for at least two weeks after sustaining a serious facial injury in a training-ground collision with Tal Ben Haim.
Chelsea boss Grant, who encountered several injury problems since taking over from Jose Mourinho last year, lamented another fresh setback to his goalkeeping staff.
"The news is that is doesn't look so good for the moment with Carlo but we need to wait and see," said the Israeli after the Fenerbahce game.
"This year I am more a doctor than a manager, I need to answer every week about injuries."
Confidence in Hilario
Despite the crisis, Grant backed Hilario and 18-year-old Rhys Taylor to handle the tough job of guarding Chelsea's goal in the upcoming crucial stage.
"We have Hilario and have the goalkeeper from the youth team. He is a good goalkeeper," he added.
"It is very important for a third goalkeeper to do a good job when you need him, and we have needed him this year.
"It's not easy when you lose your goalkeeper. Hilario was good."
Portuguese goalie Hilario was involved in some first team action last season under Mourinho, but the 32-year-old failed to impress.