Ford offered no apologies a day after the clip, which shows him using Jamaican swear words and other profanities, at one point aiming his curses at Toronto's police chief, was posted anonymously to YouTube.
"Monday was unfortunate," he said at a late afternoon news conference. "I had a minor setback. We all experience these difficult bumps in life."
But, he said, it is a "completely private matter."
"As you know I'm a human being, the same as every one of you and I'm entitled to a personal life," Ford said. "My personal life does not interfere with work I do day in and day out for the taxpayers of this great city."
The poorly framed video of the largely incoherent Ford using Jamaican swear words appears to have been filmed at a restaurant called Steak Queen in the city's north west.
Ford refused to answer reporters' questions throughout the day about whether he drove himself to or from the restaurant that night, if he was using drugs and if he was hanging out with his friend, Alexander Lisi.
A second video also posted to YouTube, purportedly from the same night, appears to show Ford sitting with Lisi — who police charged last year with extortion, alleging he tried to get his hands on the infamous video that appears to show Ford smoking crack cocaine.
Ford spent much of his news conference discussing the city's budget and finished by saying he would be "happy to take questions on the budget only," but he would not be answering any personal questions.
He walked off the moment a reporter asked if he had been on drugs Monday night.
Ford dismissed suggestions that his actions were affecting city hall business.
"I am telling the Toronto residents that I'm still working hard every day to improve my health and my well being," he said.
Premier Kathleen Wynne said she was concerned Ford's personal problems were taking attention away from the real issues facing Canada's largest city.
"To the degree that this discussion about one person's personal issues can detract and distract from the business of growing Toronto and making sure that Toronto is the best that it can be, then that does concern me," said Wynne.
"So I hope that Rob Ford is able to get the personal support that he needs."
Coun. Denzil Minnan-Wong said he agree the mayor is entitled to a private life, but pointed out that in this case the mayor was not in a private place.
"If this were happening at home in the privacy of his own home with his family I don't think anybody would care, but since this is happening in a public place it's a little bit different," he said.
"He is the mayor. He's under additional scrutiny."
Ford's admission that he had been drinking ended weeks of adamant vows that he had given up alcohol.
He had repeatedly said he hasn't had a drink since November — after a month in which reams of allegations in police documents that he did drugs, drove drunk and consorted with gang members were released by the courts.
The mayor has denied those allegations, which have not been proven in court, but did admit in November that he had smoked crack cocaine, likely in one of his "drunken stupors."
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