The Oscar-winning star – who appeared in films including The Silence Of The Lambs, The Elephant Man and Legends Of The Fall - spoke to an audience in Los Angeles about his life and career.
The 80-year-old said he was very difficult to work with in the early stage of his career "because he was usually hung over".
Sir Anthony added he had been "disgusted, busted and not to be trusted" while he was drinking.
The Welsh actor told how he turned his life around following a talk with a woman from Alcoholics Anonymous in December 1975.
He said the woman asked him, "why don't you just trust in God?" and from then on the urge to drink was "never to return".
He told the students that he can't believe his life is the way it is now because he should have "died in Wales, drunk or something like that."
Sir Anthony recently starred in HBO drama Westworld and will appear in the Netflix's The Pope where he stars as Pope Benedict.
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