Amid speculation the 38-year-old's arrival at the A-League club was the catalyst for Crook's decision, Del Piero released a statement - in Italian - on his site expressing his sympathy at the departure of the English coach after just six games at the helm.
"I'm sorry for the resignation of our coach Ian Crook. In the few months here in Sydney so far, I could appreciate the quality of technical and human resources. His is a personal choice and should be respected, I can only wish him the best future," the statement read.
"As for the team, of course we are going through a difficult time but I know that the great successes also pass through the ability to learn to react and come out from complicated situations, where everything seems to be going wrong.
"In my career I have faced so many times like we are experiencing today, and it is vital to keep our nerve and continue to train hard and well, trying to keep an open mind and trying to think positive."
Sydney are yet to appoint a permanent replacement for Crook, with assistant Steve Corica to be in charge for their trip to Brisbane Roar on Friday night.