Baroness Chakrabarti took her seat in the upper chamber on Tuesday.
Interviewed by Simon Johnson, chief executive of the Jewish Leadership Council, she said: "It has not been the most pleasant summer of my life but you can't run away from issues."
The former director of human rights group Liberty defended her integrity and said if she were asked again, she would still carry out the investigation into antisemitism.
Baroness Chakrabarti said: "I knew antisemitism on the left and in the Labour Party was a problem.
"That is why I said yes to do the inquiry in the first place and I would do it again."
It was unfair, she argued, to label the inquiry a "whitewash". Clinging to a copy of the 20-page document she added: "I think I would ask people to read my report and engage with it."
Baroness Chakrabarti also denied reports she had missed a deadline set by the Home Affairs Select Committee to explain conversations she had about the peerage with Labour leader Jeremy Corbyn. She said she explained herself to former committee chair Keith Vaz.
The audience listened silently as she told them the peerage had not been "a happy thing" because of the abuse she received since it was announced.
"It has not been the happiest moment of my life but it hasn't been the worst either. I am not a refugee drowning in the Mediterranean. So I will suck it up and do my best."
The peer said it was of "great regret" the party had not yet implemented the recommendations she made in the report.
One Prestwich resident asked if Baroness Chakrabarti felt not being Jewish had hindered her ability to understand antisemitism.
Baroness Chakrabarti replied: "I don't know what it is like being Jewish, in the same way you don't know what it is like being me. I don't know what it is like to be called a 'Yid' either, but I do know what it is like to be called a 'Paki', so there are similarities."
Baroness Chakrabarti was asked by the JC why she had not made any reference in her report to evidence submitted by Joshua Simons, a Jewish former policy adviser in Mr Corbyn's office who said the leadership had "at least a blind spot with antisemitism and at worst a wilful disregard for it".
She said the omission of his name had been a matter of confidentiality. Mr Simons has gone public with his evidence since the report was published in June.
As the meeting concluded, the baroness made a hasty exit, and was ushered into a waiting taxi by an aide.
Audience member Keith Fairclough, who travelled from Liverpool, said: "I think she was brave and at least she turned up.
"She was too liberal and let too much go in the inquiry itself. She should have been stronger on a lot of things."
Following the event , Mr Johnson said: "She knew what she was doing. The audience can judge her for themselves.
"I think she warmed up, her body language at the start was very defensive but softened when she realised they weren't out to get her."
