Vincenzo Dallaglio, 60, and his wife Eileen, 57, said they were "bitterly disappointed" by the sum Mr Justice Latham awarded, pounds 33,930, for the loss of their daughter, Francesca, who they had described as the "sole breadwinner" in their family.
Mrs Dallaglio added that it was "morally wrong" that their award would be used up in legal costs leaving the owners of the two boats to "get away with it scot-free".
Francesca,19, was on the brink of a career as a ballet dancer when she died, along with 50 other young people after the dredger Bowbelle collided with the Marchioness on 20 August 1989 in mid-stream of the river Thames.
The owners of the two vessels admitted liability for damages five years ago and the judge was asked only to assess how much should be awarded. Other death and personal injury claims have been dealt with by the Registrar of the Admiralty Court, including a pounds 15,000 award for the loss of a daughter.
The Dallaglio case was the only claim to be transferred to a judge for assessment because of the couple's heavy financial reliance on their daughter.
The boats' owners made a pre-trial settlement offer of pounds 50,000, Mr Justice Latham was told in the High Court yesterday. Because the offer was greater than the final award, the Dallaglios were ordered to pay the defence costs. As is usual in such cases, he was not told of the pre-trial offer until after his judgment.
The judge said Ms Dallaglio was a "lovely, greatly talented girl" who had just obtained her first job after dance and drama school. "It is obvious that many lives have been made the poorer by her death," he said.
In financial terms, however, there was no secure evidence that she would have provided a regular income for her financially vulnerable parents, and her mother's evidence on this was "unrealistic".
"I cannot believe that before her death they had any real expectation that she would have provided them with, in effect, a pension," said the judge. "I am sure they would have wanted her to secure her own financial position and to have provided for her family when she married and had children."
He awarded the legally aided couple pounds 16,000 for their loss, plus pounds 4,806 to Francesca's estate and pounds 13,124 interest.
Mrs Dallaglio said afterwards: "We should never have been brought to this court in the first place. When the vessel owners admitted liability, punitive and exemplary damages should have been paid immediately to all the families involved - the survivors and the bereaved ...
"These companies have taken 51 young talented lives and ruined many other lives and yet they walk away scot-free.
"If I have to dedicate the rest of my life to it, I will work to secure amendments to the law to make sure no one else is treated like this."