They spoke out following the officer being cleared of causing death by dangerous driving.
Constable David Brown, 30, broke down after the jury of 10 women and five men returned the not guilty verdict at the High Court in Glasgow yesterday.
He had been accused of causing the death of 65-year-old John Lacon by crashing his police van into Mr Lacon's Fiat Doblo in Glasgow last year.
Temporary judge John Beckett, QC, told Mr Brown: "The jury has found you not guilty, you are free to go."
The officer, who is now working in police intelligence, said: "Thank you my lord," before leaving the court and hugging his family.
However, the victim's family said the outcome had left them with a sense of injustice. They added: "The court process has been a harrowing experience for all members of the family.
"We have been disgusted at the conduct of Strathclyde Police throughout this process.
"The process has been exhausting and we have no more energy left to give it. We have been destroyed and nothing can change that."
It emerged yesterday the officer had wanted to plead to a reduced charge of causing the death by careless driving, but this was rejected by the Crown.
The jury could also have convicted him of this reduced charge, but chose not to.
The court heard Constable Brown was responding to three "officers in danger" emergency calls after a riot broke out at Kelvingrove Park during the Royal Wedding celebrations.
Mr Lacon sustained head injuries in the crash and died from his injuries in the Western Infirmary 12 days later.
A police spokesman said: "We deeply regret the loss of life and our sympathies are with Mr Lacon's family. It would be inappropriate however, to comment on a decision which has been taken by a jury as part of the judicial process."