The search will go on to find out what really happened on the night UK student Meredith Kercher was murdered in Italy four years ago, her family has said.
Speaking after an Italian court cleared Amanda Knox and Raffaele Sollecito of murder, Meredith's brother Lyle said it felt like it was "back to square one".
Prosecutors say they will appeal. Rudy Guede, 24, - still convicted of the murder - is to seek a retrial.
Knox has left Italy and is on her way to her hometown of Seattle in the US.
She is travelling back to her hometown of Seattle on a commercial flight and is expected to land at around 0100 BST on Wednesday (0000 GMT, 1700 PDT on Tuesday).
Speaking to reporters in Perugia, where his sister was studying at the time of her death, Mr Kercher said: "We accept the decision and respect the court and the Italian justice system.
"We do find we are now left looking at this again and thinking how a decision that was so certain two years ago has been so emphatically overturned, which raises other questions.
"It feels very much like back to square one. The search goes on to find out what really happened."
During a separate earlier trial, Guede was convicted of Miss Kercher's murder and sentenced to 30 years in prison. On appeal, his conviction was upheld but his sentence reduced to 16 years. A lawyer for Guede on Tuesday said he would seek a retrial.
It was said in court that Guede did not act alone - raising questions following the acquittals as to who had also been at the murder scene.
Meredith's sister, Stephanie, said the "biggest disappointment" was still not knowing what happened and knowing "someone or people out there" were responsible.
"It's still very difficult to speak in terms of forgiveness," she added.
"Until the truth comes out, we can't forgive anyone because no-one's even admitted to it knowing there was someone out there who was responsible."
Their mother, Arline, said: "What happened to my daughter, Meredith, is every parent's nightmare.
"Of something so terrible happening, when basically she was in the safest place, her bedroom."
Prosecutors said Miss Kercher was killed in a brutal sex game which went wrong.
Mrs Kercher admitted she could appreciate why Knox would feel she had lost her life over the last few years.
"I don't think anyone's going to get off scot-free," she said. "Their lives have been disrupted - no-one is untouched by this."
Earlier, UK Prime Minister David Cameron said he felt sympathy for the Kerchers.
"They previously had an explanation about what happened to their daughter and they don't have that any more, and I think all of us should be thinking of them," he said.
Knox, 24, and Mr Sollecito, 27, spent nearly four years in jail but their convictions were overturned on Monday after evidence was found to be unreliable.
The prosecution is to appeal to Italy's highest court, although it appears unlikely that Knox would be extradited back to Italy from the US.
An eight-member jury cleared both defendants of Miss Kercher's murder after doubts were raised over procedures used to gather DNA evidence.
The judge upheld Knox's conviction for slander for accusing bar owner Patrick Diya Lumumba of carrying out the killing. But he set the sentence at three years, time that Knox has already served, meaning she was free to leave.
She was ordered to pay him 22,000 euros (£18,800) in compensation.
Her family said she had "suffered for four years for a crime she did not commit".
Speaking on the steps of the court, Knox's sister Deanna said: "We are thankful to the court for having the courage to look for the truth and to overturn this conviction."
She said her sister's "nightmare was over" and asked for privacy for her family to recover from "this horrible ordeal".
Knox's lawyer, Carlo Della Vedova, said outside court that there was "no winner" in the case and the appeal court had "rectified a mistake".
"Meredith was a friend of Amanda - we should never forget this and we have to respect the sorrow of all the families," he told the BBC.
Mr Sollecito's father Francesco said he had "allowed himself some tears" following the verdict and said the court had "given me back my son".
Hundreds of people had gathered in the streets outside the court ahead of the verdict and some shouted "shame" when they heard about the decision, while others cheered.