Speaking at a press conference in Florence, 21-year-old Kercher's brother Lyle and sister Stephanie said they could not draw a line under her death while the process was going on.
They called for Knox to be extradited from the US and declined to comment on reports that Sollecito had been arrested by Italian police close to the Austrian border.
"I think we are still on a journey for the truth and it may be the fact that we don't ever really know what happened that night, which is obviously something we'll have to come to terms with," Stephanie said.
"You can't ever really get to a point where you just start to remember Meredith solely because it is following the case, coming over to Italy and everything associated with it.
"But the verdict has been upheld this time so we hope that ... we are nearer the end so that we can just start to remember Meredith for who she was and draw a line under it, as it were."
Knox has said she will only be extradited to Italy "kicking and screaming", after judges reinstated her murder conviction yesterday for the death of Miss Kercher.
Knox, who stayed in her native US for the trial, was sentenced to 28 years and six months and her former boyfriend Sollecito was jailed for 25 years.
Kercher, a Leeds University exchange student from Coulsdon, south London, was found with her throat slashed in the bedroom of the house she shared with Knox in Perugia, central Italy, in November 2007.
When asked if Knox should be extradited, Lyle Kercher said: "If somebody is found guilty and convicted of a murder and if an extradition law exists between those two countries, then I don't see why they wouldn't.
"I imagine it would set a difficult precedent if a country such as the US didn't choose to go along with laws that they themselves uphold when extraditing convicted criminals from other countries.
"It probably leaves them in a strange position not to."
Amanda Knox's ex-boyfriend Sollecito detained near Austrian border
Meanwhile, Raffaele Sollecito, Amanda Knox’s Italian former boyfriend, has been detained in a village just by the Austrian frontier and is currently in a police station, Italian media reports.
Italian news agency ANSA said the 29 year-old Sollecito had been located by police officers in a village between Udine and the town of Tarvisio, close to the Austrian border.
The agency said that in the early hours of this morning Sollecito had been warned that he was forbidden to leave Italy. According to other media reports, his passport was taken away from him, as ordered by the Florence court.
Lawyers for both Knox and Sollecito have said previously they will appeal to the supreme Court of Cassation.
More details to come.