Families are allowed six visits a month and those from outside Italy generally get two extra.
But Christmas doesn't fall on a visiting day so Knox will attend mass in the prison with fellow inmates, reports CBS News correspondent Allen Pizzey.
"She had her tough moments. There were some tears just because she wants out of there and she's just really scared that this mess is not going to get fixed," Mellas said.
Mellas said the family has been "devastated" by the conviction but Knox is "trying very hard to make the best of it."
Since the conviction, which resulted in a 26-year sentence, Knox has received a surprising amount of support. A merchant from nearby Assisi has collected Christmas gifts for her.
She's also received what her family says are hundreds of letters, nearly all of which are supportive.
"It's really been amazing … to see that so many people realize that this is kind of a big mistake and they're all just telling us to hang in there," Mellas told CBS' "The Early Show Monday.
Mellas said Knox has found prison life "boring" and spends a lot of time reading and writing.
Knox and her former boyfriend Raffaele Sollecito, who was sentenced to 25 years for his part in Kercher's murder, reportedly exchange letters along the lines of "Hang in there, the truth will come out eventually."
Knox recently told a visitor she was "scared" of being in jail but her appeal can only begin when the judge releases the written motivation for the guilty verdict, which is expected to happen by March 5.
"That was one of the things that she expressed a fear today of having to stay in there and I really truly believe that this mistake will get fixed," Mellas said. "It's taking way longer than we thought, but we believe that."