The Hoops will be hoping to complete the double when they face Hibernian in the final at Hampden on Sunday, having already secured the SPL title.
Neil Lennon's men also impressed on the continental stage this term by reaching the last 16 of the Champions League, but van Hooijdonk says Celtic will fall short of domestic expectations if they are unable to add to a championship trophy they were expected to win.
He said: "I think in this league, in this year, everybody expects Celtic to win at least two of the three trophies. There are a lot of people who expected them to win all three. If you lift only one trophy this year, I think people will see it as a bit of a disappointment."
One of van Hooijdonk's own finest moments in a Celtic jersey was his winner against Airdrie in the 1995 Scottish Cup final - ending a barren spell of six years without silverware at the club.
Back in Glasgow on Thursday to help promote Sunday's clash, he said: "It brings back good memories of 1995 when I was playing for Celtic and we won the cup final.
"I've scored better goals but not many more important than that goal. I know what it means to the fans to get some silverware.
"Of course, the championship is already in the pocket so it would be nice for them to get the second trophy."
The former Nottingham Forest and Feyenoord forward believes Celtic's ambitions are being restricted by the league they compete in. And he admits he would love to see them given the opportunity to join the Barclays Premier League in order to fulfil their potential.
Van Hooijdonk said: "They cannot grow any more. They are massive off the field and need to make bigger steps on the pitch now and they can't. It's all about money and the TV money that helps you. If Celtic were to enter the Premier League, they would become massive."