Spencer Kuvin, who represents several unnamed alleged victims, said “royalty has failed them”.
The prince has stood by his decision to take part, despite critics describing it as a “car crash”.
The duke has been facing questions over his ties to Epstein for several months.
On Monday, Mr Kuvin told the Today programme: “It was depressing that he [Prince Andrew] really did not acknowledge the breadth of his friendship with this despicable man and apologise.
“The mere fact that he was friends with a convicted sex offender and chose to continue his relationship with him – it just shows a lack of acknowledgement of the breadth of what this man [Epstein] did to these girls.”
But Mr Kuvin said he did “not think there was any way” the prince could have avoided seeing what was going on, “with young girls being shuttled in and out of those homes”.
Mr Kuvin said the focus of Epstein’s accusers had now turned to potential co-conspirators.
It has led to questions about the role Epstein‘s former girlfriend, Ghislaine Maxwell, may have played in procuring underage girls for the financier.
Ms Maxwell denies any wrongdoing.
She told the BBC’s Victoria Derbyshire programme: “I think he’s made things worse for himself in this interview and I think it’s more likely the authorities are going to want to speak to him now – and they should want to.”
Gloria Allred – another lawyer, also representing one of Epstein’s accusers – told ITV’s Good Morning Britain: “Now he’s been in the court of public opinion, he should testify to the FBI.”
She said she did not know how the prince “could have not known that there were underage girls” present during his visits to Epstein’s homes in New York, Palm Beach and the Virgin Islands.
Meanwhile, Labour’s shadow trade secretary, Barry Gardiner, said Prince Andrew should do whatever he can to help Epstein’s victims.
He said: “By saying what he knows of the time that he spent with his former friend, can only be the right thing to do.”
In the Newsnight interview, Prince Andrew said he will testify under oath “if push came to shove” and his lawyers advised him to.
It comes as the prince continues to face heavy criticism for the interview, which many royal commentators branded a PR disaster.
In his BBC interview, Prince Andrew “categorically” denied having any sexual contact with Virginia Giuffre, known at the time as Virginia Roberts.
The first occasion, she said, took place when she was aged 17.
People close to Prince Andrew said he wanted to address the issues head-on and did so with “honesty and humility” in speaking to Newsnight.
- On the date Virginia Giuffre says he had sex with her – 10 March, 2001, he had taken his daughter to Pizza Express in Woking for a party before spending the night at home
- He dismissed claims he was sweating profusely because he had a “peculiar medical condition” meaning he cannot sweat, caused by an overdose of adrenaline in the Falklands War
- He had commissioned investigations into whether a photograph of him with Ms Giuffre had been faked, but they were inconclusive
- Speaking out about his relationship with the financier had become almost “a mental health issue” for him
- He would testify under oath about his relationship with Ms Giuffre if “push came to shove”, and his lawyers advised him to
- He was unaware of an arrest warrant against Epstein when he invited the financier to Princess Beatrice’s 18th birthday party at Windsor Castle
- He did not regret his friendship with Epstein because of “the opportunities I was given to learn” from him about trade and business