In his first TV interview since charges were dropped, the ex-IMF chief said he regretted the affair had lost him his chance to stand for French president, but denied using violence.
He said he had been afraid and humiliated by the US justice system. Mr Strauss-Kahn, 62, resigned as IMF chief in May after his arrest.
The maid, Nafissatou Diallo, is bringing a civil suit against him. The criminal charges were dropped in August when prosecutors said Ms Diallo's lack of credibility meant the case could not continue.
Mr Strauss-Kahn was questioned by Claire Chazal, a friend of his wife Anne Sinclair, on the main Sunday night bulletin of France's TV1 - watched by a huge audience.
"What happened was more than an inappropriate relationship. It was an error," he said, adding that he regretted it infinitely.
"I think it was a moral failing and I am not proud of it," he told Ms Chazal. He said the incident had caused him to miss his "appointment with the French people", referring to his desire to be a Socialist candidate in France's 2012 presidential elections.
Before his arrest, he had been expected to be a strong contender to challenge President Nicolas Sarkozy.
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