She was speaking at the end of the TRC special hearing in Mayfair, Johannesburg, into human right atrocities allegedly perpetrated by her and the Mandela United Football Club, who acted as her personal bodyguards in the late 1980s.
Madikizela-Mandela answered damning allegations against her by resorting to blanket denials and claims that testimony from several witnesses over the marathon nine-day hearing was "ridiculous", "ludicrous" and "fabrications".
Her apology followed an emotional appeal from TRC chairman Archbishop Desmond Tutu for her to say sorry.
"You are a great person and you do not know how your greatness would be enhanced if you said `sorry, things went wrong for me'," Tutu said.
He said he had immense admiration for Madikizela-Mandela, calling her an icon and a stalwart of the liberation struggle.
"We can never forget her contribution... and her indomitable spirit. And yet one has to say something went horribly wrong. What, I don't know."
It was clear something had gone wrong, because many Mass Democratic Movement leaders became involved in seeking a solution to the problems flowing from the criminal conduct of the football club.
Tutu said: "I speak to you as someone who loves you very, very deeply, who loves your family very deeply. There are people who want to embrace you. There are many who want to do so, if you were able to say `something went wrong' ... and say, `I'm sorry, I'm sorry, for my part in what went wrong'.
Tutu concluded: "I beg you, I beg you, I beg you, please, I have not made any particular finding about what happened. You are a great person and you do not know your greatness will be enhanced if you said,`sorry, things went horribly wrong'."
Madikizela-Mandela, who consulted with her attorney during Tutu's appeal, hesitated and then replied: "I will take this opportunity to say to the family of Dr Asvat how deeply sorry I am."
She also apologised to the mother of slain teenage activist Stompie Seipei.
Tutu was also instrumental in initiating reconciliation with Joyce Seipei, mother of Seipei. Her son's convicted killer, Jerry Richardson, said during the hearing he killed the teenager on Madikizela-Mandela's instuctions. Madikizela-Mandela denied this.
The reconciliation followed an incident in the public toilet at the venue, where Mrs Seipei was allegedly harassed and intimidated by women wearing the uniform of the African National Congress Women's League, of whom Madikizela-Mandela is president.
Proceedings were interrupted when Tutu called Mrs Seipei, who was seated in the audience, to the front of the hall, where she and Madikizela-Mandela embraced and kissed.
Madikizela-Mandela was convicted and fined for kidnapping Stompie. Her lieutenant, Richardson, stood alongside Mrs Seipei as cameras flashed and the public gallery applauded.
Tutu called on other relatives of victims and former associates of Madikizela-Mandela, including Dudu Chili and Xoliswa Falati, to come forward.
Tutu said: "We all stand here to recognise the pain and anguish of so many. We want them to know they have our very deepest sympathy for what they suffered.
"We hope they have it in their hearts to reach out to those who may have caused them pain, to reach out in order for our land to be healed."
But the moment was deemed inappropriate by one of the victim's legal representatives.
"How can there be reconciliation unless there is some acknowledgement of the violence that has been committed?" asked one advocate, who said he may not be named for professional reasons.
"People want to know what has happened to their families. They live with the pain of not knowing. Reconciliation is all very well, but now there is at least some doubt as to whether Madikizela-Mandela is telling the truth or not.
"I think the moment chosen for this reconciliation, when she was not answering questions satisfactorily, was completely inappropriate," he said.
Also unimpressed by thoughts of reconciliation was Caroline Sono, mother of missing Soweto youth Lolo Sono, who on Thursday demanded that Madikizela-Mandela tell her what had happened to her son.
In an emotional outburst outside the hearing, Sono screamed: "She's the woman who murdered our children. I will not rest until I find my son's remains. I want Lolo."
Her husband, Nicodemus Sono, told the TRC last week he last seen his son alive, badly beaten, in Madikizela-Mandela's company. Madikizela-Mandela described Sono as a courier for the African National Congress during its armed struggle against the apartheid government.
Richardson told the TRC he killed Sono - and Siboniso Shabalala, who was allegedly with the beaten Sono - on the instructions of Madikizela-Mandela. The bodies of the two youths have not been found.
"I think nothing about the TRC session," Caroline Sono said. Nothing has been done. There's no justice in this land. Stompie's being found, Asvat's been buried, Kuki Zwane was found and buried... where is my son?"
Madikizela-Mandela denied on Thursday she had any part in Sono's disappearance.
Madikizela-Mandela's blanket claims of innocence to the numerous allegations against her prompted truth commissioner Yasmin Sooka to describe her testimony as "particularly painful".
Most painful, said Sooka, were Madikizela-Mandela's attempts to discredit leading figures of the anti-apartheid struggle, who tried to persuade her to distance herself from the football club's violent activities.
"If we believe your evidence, then everyone is lying," said Sooka.
Madikizela-Mandela replied: "Yes, it's true most witnesses were lying. As far as I'm concerned, Richardson was lying. The two youths who claimed I ordered them to kill Dr Asvat were lying. (John) Morgan's ludicrous statements are a pack of lies. I can go on, and on."
The witnesses made various allegations against Madikizela-Mandela, including some linking her to murders. She dismissed them as ludicrous and ridiculous.
The allegations included that she and her daughter Zinzi ran a kangeroo court at their Diepkloof home, where people accused of being informers were beaten and tortured.
She said: "My daughter's name is dragged in at random on the most ridiculous allegations I have heard."
Her apology at the end of the hearing did not satisfy senior African National Congress leaders.
Safety and Security Minister Sydney Mufamadi, also an ANC national executive committee member, said: "I heard Mrs Mandela concede for the first time that something went horribly wrong. I wish she came to that realisation earlier, because perhaps this hearing would not have been necessary."
After the hearing ended, former United Democratic Front treasurer Azhar Cachalia told reporters there were sufficient grounds for prosecution, especially the case of missing youth Lolo Sono.
"I would be surprised if, given the additional information which emerged from the hearings, there aren't in fact court cases," said Cachalia, who is head of the secretariat of the Safety and Security Ministry.
Addressing reporters after the hearing, Sooka said Madikizela-Mandela's accountablity was not adequately addressed.
"The apology was helpful, but at the end of the day the question of accountability has to be addressed," Sooka said.
Mpumalanga premier Mathews Phosa said the ANC would make a full statement in due course.
Also likely to feel dissatisfied were the lawyers for the victims.
After eight days of damning allegations against Madikizela-Mandela, through most of which she sat stone-faced and emotionless, she took just over an hour on Thursday morning to proclaim her innocence on all the allegations.
Lawyers who had been waiting all this time to question her found their cross-examining cut short by Tutu, who allocated short periods of time to each lawyer, and strictly enforced the allotments.