The BBC Radio Scotland pundit injured his arm and suffered bruising as he tried to stop the thief fleeing in his S-Type Jaguar by clinging on to the bonnet.
But Mr Young, 61, said that although he had identified who he thought the robber was, it was not enough for prosecutors to go ahead with the case.
It is understood the charges were not pursued after a witness was unable to provide alternative evidence that would allow the case to go ahead.
Mr Young supported Scottish Government moves to abolish corroboration, which requires at least two independent pieces of evidence for a conviction to succeed.
He said: "I am far from happy, but what can I do?
"I identified a man. He broke into the house, took my car keys and I caught him stealing the car.
"For me it (corroboration) is a flaw in the law, which I believe is being addressed. The timing is not good for me, but it is a classic example of why they should try and do something about it."
Steven Connelly, 30, who was charged with breaking into Mr Young's home in Pollokshields on September 13 last year, was due to stand trial yesterday at Glasgow Sheriff Court before the case against him was dropped.
Connelly, also of Pollokshields, was accused of stealing an iPad, laptop, a signet ring given to Mr Young by his mother, a watch and his late son's bracelet from his home. He also allegedly stole the Jaguar.
Connolly maintained his pleas of not guilty to all the charges.
Mr Young said: "I can be disappointed but I am sure the procurator fiscal's office are as upset as I am. It would have been a waste of the court's time, apparently."
The only item recovered was the ring, which was found down the seat of a car owned by a fellow BBC employee that had been broken into 1½ miles from Mr Young's home.
A Crown Office spokesman said: "After full and careful consideration of all of the available evidence, the procurator fiscal instructed there could be no further proceedings."