Third-choice stopper Hilario came off the bench to replace Cudicini during the Champions League tie at Stamford Bridge on Tuesday.
The Portuguese pulled off fine saves from Gokhan Gonul and Colin Kazim-Richards, and Grant stressed he has full confidence in Hilario as he faces up to a goalkeeping crisis.
"It is very important for a third goalkeeper to do a good job when you need him, and we have needed him this year," said the Chelsea boss after the 3-2 aggregate win which saw his side progress to the Champions League semi-finals.
Grant added: "This year I am more a doctor than a manager, I need to answer every week about injuries.
"We have Hilario and have the goalkeeper from the youth team. He is a good goalkeeper."