Lucie Blackman's father says she has been "robbed of justice" after a man was cleared of raping and killing her.
But Japanese businessman Joji Obara, 54, was jailed for life for raping nine other women, including one - Australian Carita Ridgway - who died.
The judge said there was no proof Obara alone was responsible for the death of Miss Blackman, 21, of Sevenoaks, Kent, who was found dead near Tokyo in 2001.
Mr Blackman said prosecutors should "strongly consider" an appeal.
Mr Blackman, from the Isle of Wight, said he was initially fairly pragmatic after the verdict because he knew that Obara had at least been locked up for life.
1 Jul 2000: Lucie Blackman vanishes in Tokyo
21 Jul 2000: Tony Blair meets Lucie's parents and promises to raise their daughter's disappearance with Japan's PM
11 Oct 2000: Japanese police arrest and question Joji Obara, who is in custody in connection with several other rapes
9 Feb 2001: Police find Miss Blackman's body parts in a cave at Miura, near Tokyo.
27 Nov 2003: Obara goes on trial in Tokyo
24 Apr 2007: Obara acquitted of killing Miss Blackman
However, he added: "Following a meeting with the prosecutors, we feel very much more upset about it and feel that in many respects Lucie has been robbed of her justice."
Mr Blackman, who was in court along with his other daughter Sophie, said evidence which had been known about for years had not been presented at the trial.
He told reporters: "We believe our family deserves to get proper justice for Lucie."
Miss Blackman's mother, Jane Steare, who was not present in court, said earlier: "I'm heartbroken. I just can't believe this. My worst fears have come true.
"I just feel that the last six years have gone by and there's no resolution. I don't really know where to go from here."
She told the BBC nothing could bring her daughter back and said the tragedy was something she would have to live with.
Ms Steare, who has been to Japan seven times, said she decided not to travel for the verdict because she did not want to have an image of Obara in her mind for the rest of her life.
Miss Blackman was working in a Tokyo bar when she vanished in July 2000.
Her dismembered body was found in a cave near Obara's home, in the village of Miura, in February 2001.
BBC Tokyo correspondent Chris Hogg said that under Japanese law the Blackman family themselves had no right to appeal against the court's decision.
They could try to mount a form of civil action but as Obara has been declared bankrupt there would seem to be little point.
Our correspondent said Obara showed little emotion as the judge told him he would be sentenced to life in prison for killing Carita Ridgway in 1992 and eight other rapes.
Samantha Termini holds a picture of her sister, Carita Ridgway
Obara lured Miss Ridgway to his apartment just south of Tokyo, where he drugged her and raped her. She later died in hospital of liver failure.
A video seized from his home showed him attacking Miss Ridgway and using a towel soaked with chloroform to keep her unconscious.
Miss Ridgway's mother, Annette Foster, welcomed the conviction but criticised the Japanese police.
"If Obara had been investigated in 1992, it would have stopped the crimes he committed for the next eight years," she said.
Obara admitted he had been with Miss Blackman on the day she disappeared but claimed she became unwell at his apartment after taking drugs.
He said he then called an acquaintance, known by the nickname Kacchan, and asked him to take her back to Tokyo. Kacchan has since died which meant his story could not be challenged.
Judge Tsutomu Tochigi said: "There is nothing to prove that [Obara] was involved in the rape and her death. The court cannot prove he was single-handedly involved in her death."
Joji Obara has been given a life sentence
The judge said it was clear Miss Blackman and the accused were together before she vanished and then died but he said this was not enough to secure a conviction.
Obara's lawyer, Yasuo Shionoya, said his client would lodge an appeal against his conviction in the Miss Ridgway case.
"Regarding Carita's case, I think we will have to file an appeal. It's very plausible that we would file an appeal in the other cases as well," said Mr Shionoya.
Last year Mr Blackman accepted 100 million yen (£450,000) from a friend of Obara, but he denied it was "blood money" and said such "offers of condolence" were common in Japan and did not affect the court case.