The involvement of family places difficult legal constraints on care providers, leaving the teenage and child victims "in a perilous state", the agency said.
They also have serious concerns about the growing number of young people reporting rape and other sexual assaults, as one in five callers to the DRCC's 24-hour helpline last year was aged 15-17.
"This is a worrying trend and indicates the need for the adequate provision of services to protect and support these young people," the centre's clinical director Angela McCarthy said.
However, she said rape crisis centres were limited in the services they could provide to adolescents without parental consent.
"It can create problems where cases might involve allegations of abuse against a father, for instance. In such circumstances, we normally have to refer people seeking help to the authorities and agencies dealing specially with young people," said Ms McCarthy.
The annual DRCC report highlighted how young people are more at risk of suffering serious sexual assault by a close family member than a complete stranger.
Just 5% of child sex abuse cases reported to the DRCC last year involved acts committed by a stranger, while most involved a close relative.
In contrast, 37% of all reported rapes and sexual assaults among adults were committed by strangers, while 42% of cases involved a friend and 10% a husband, partner or boyfriend.
The chief executive of the Irish Society for the Prevention of Cruelty to Children, Paul Gilligan, said there was a need for a clear legal interpretation over the role of the caring services, given the constitutional protection given to parents.
Overall, the total number of calls to the DRCC relating to adult rape and sexual assault rose from 53% to 57% in 2003. The increase was also reflected in the numbers availing of the centre's counselling services, with 62% having suffered rape or sexual assault last year compared to 59% in 2002.
A total of 11,863 counselling calls were received by the DRCC last year up slightly on the 2002 figures.
The centre also had to close its waiting lists for short periods last year due to a shortage of therapeutic services as it provided counselling for a total of 624 clients.
DRCC chairperson Breda Allen appealed for more funding for services provided by rape crisis centres. She said the groundbreaking Sexual Abuse and Violence in Ireland (SAVI) report had revealed that sexual violence of all types had been reported by more than one million citizens.
"It is clear the services are not adequate if even 20% of these people were to seek them," said Ms Allen.
In another worrying trend, clients using the DRCC's services last year indicated a declining willingness to report their case to the gardaí. Only 30% of victims of rape and sexual assault said they had notified the authorities of the crime, compared to 33% in 2002.