Prosecutors say they plan to try Cosby again. "If I am called upon to do my civic duty, I will do it", she said. But Allred, who represents Kirkpatrick and 32 other accusers, said she hopes he will reconsider.
She said the incident left her "humiliated" by someone she had thought of as a friend and mentor.
Spokesman Andrew Wyatt said Saturday that "Cosby's power is back".
Cosby remained stoic, while Constand embraced the person next to her. Her parents noticed a change in her personality and that she had trouble sleeping.
The jury had been instructed by the judge to work into the weekend to reach a verdict, after they first revealed that they were deadlocked on the case on Thursday.
BLOCK: After the mistrial was declared, Bill Cosby appeared outside the courthouse. He described their previous encounters as "social and romantic". The district attorney at the time declined to press charges, citing insufficient evidence.
The next month, Constand filed a lawsuit claiming battery, sexual assault, intentional infliction of emotional distress and other claims.
TAYLOR: Unfortunately, while I am disappointed, I am not surprised that you could not find 12 jurors based on the facts and evidence in this case who would convict Bill Cosby of rape. Prosecutors have suggested he gave her something stronger, possibly quaaludes.
Cosby's team immediately went on the attack.
Cosby's alma mater, the University of MA at Amherst, cut ties with him, the first in what would become a long list of organizations to do so.
Meanwhile, attorney Gloria Allred, who represents numerous Cosby accusers, said the entertainer's fame carried its own power. But if you remind yourself, Mr. Cosby put on a single witness for six minutes in this case as his defense.
The jurors also asked the court to define a phrase in one of the charges, to define "reasonable doubt" and to rehear what a detective testified to about Cosby's interview with police in 2005.
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NPR host Scott Simon filled the airtime by saying Cosby was just "shaking his head no". Cosby's wife, Camille - who skipped all but the defence closing argument - issued a blistering statement Saturday. "This was about him and he was not going to allow them to be shields".
The prosecution spent five days painstakingly trying to build their case, calling Constand and her mother to the stand, as well as another woman who alleged that Cosby also drugged and assaulted her in Bel Air in 1996. She sued Cosby in a civil suit and settled for an undisclosed amount in 2006.
District Attorney Kevin Steele said Friday he would push for a retrial as soon as possible, reassess the case and possibly make some "tweaks".
The case has helped demolish Cosby's nice-guy image, cultivated during his eight-year run as Dr. Cliff Huxtable on the top-rated "The Cosby Show" in the 1980s and '90s.
Cosby was arraigned in December 2015.
But early reaction to the Cosby mistrial from the celebrity twitterverse was decidedly muted.
Cosby's trial started June 5 in Norristown, Pennsylvania.
Prosecutors argued Cosby drugged and sexually assaulted Constand. If found guilty he could have faced up to 10 years in prison on each charge.
In Norristown, Pennsylvania, the jury struggled for days to agree on which version of the night in question to believe: Constand's or Cosby's.
It's possible the next jury could be selected in another county so as not to place too heavy of a burden on Allegheny County, where Pittsburgh is located, said Dennis McAndrews, a former Philadelphia-area prosecutor.
It was the only criminal case to arise from allegations from more than 60 women that cast Cosby - married more than 50 years - as a serial predator who gave drugs to women before violating them.