The actor admitted he was stunned when the message he left for his 11-year-old daughter was made public.
Speaking on news show 20/20, Baldwin told Sawyer, "It (message) was left with the presumption of privacy."
And when the interviewer suggested the angry message, in which Baldwin called his daughter "a thoughtless little pig," was uncalled for, the movie star became angry.
He asked, "Why do you so reflexively dismiss that notion? I mean you carelessly dismiss that notion."
Sawyer tried to protest, asking Baldwin how he felt as a father after the message was made public.
He responded curtly, "There are a myriad of both men and women who say things that are unfortunate and are mistakes to their children."
The emotional interview led to tears as Baldwin recalled feeling so low after the controversy of the leaked answering machine message that he contemplated suicide.
Wiping tears away, he told Sawyer, "I completely lost interest in my own life, truly, as a result of all this.
"I used to pray to God every night, I would get in bed and I would say, 'Please don't let me wake up in the morning.' I thought, 'I just can't do it anymore.'"
In a new book, titled A Promise to Ourselves, Baldwin details just how far he went in planning his own death, searching out state parks and out-of-the-way towns where he could take his own life quietly.
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