Marie Collins, who met the senior clergyman several weeks ago in Armagh, said the cardinal would have shown much more leadership by stepping down.
"I think the Church needs new leadership and I'm disappointed that we're not going to get it," Ms Collins said. "It's not a question of revenge, it's a question of taking responsibility.
"We can't have change in the Church here until everyone in the top realises how actions of the past decimated so many lives."
Ms Collins, abused as a child in Crumlin Children's Hospital, said she was disappointed Cardinal Brady had not acknowledged in his statement that Fr Brendan Smyth had gone on to abuse children after his activities became known to the Church.
"I think Cardinal Brady is making a mistake," Ms Collins said. "I think the signal that is sent out is, 'no change, we'll keep the same leadership and we'll keep on going in the same way as we always have'."
Fellow survivor Andrew Madden said he was not surprised by the cardinal's pledge to stay in his post, adding he did not believe the cleric had any intention of resigning.
"I think they have a huge credibility problem if they try to speak, of child protection or other moral issues, when their own leadership was involved in the cover-up of the sexual abuses of children and kept it quiet for 35 years," Mr Madden said.
"It's very damaging for people on the ground who are doing child protection to see that they're doing one thing, and that the leadership is minimising what Brady did in 1975 while they're trying to be taken seriously."
Support group One in Four said victims want senior clergymen to be accountable for what they have done and resign, and accused the Archbishop of Armagh of not listening to survivors.
The group said that in the week of the anniversary of the Ryan Report it was sad that so little of substance has changed in the Church.
The organisation said Cardinal Brady's stance made it difficult to believe there had been any real change and urged him to ensure that every member of the Catholic Church prioritised child protection.
SIC: II