The former prime minister made the admission during a segment of ABC's The House with Annabel Crabb, set to air on September 5.
Mr Abbott, who was leader of the opposition in 2009, said he had consumed "quite a few bottles of wine" with Peter Costello and Kevin Andrews on February 12, the night of the crucial vote.
“Peter was close to leaving at that stage, and I think all of us were in a mellow and reflective mood, so the reflections went on for longer, and later, than they should have," Mr Abbott told Ms Crabb.
“The impact was rather greater than it should have been.
“I think I famously slept through several divisions.”
Mr Abbott said he fell asleep on the couch in his office and was out for the count.
“It was a late night sitting, against all OH&S rules as you can imagine,” he said.
“I lay down, and the next thing I knew it was morning.”
The admission follows Mr Abbott being hounded by former treasurer Wayne Swan for missing the vote.
"The leader of the opposition slept right through the critical vote, he was drunk and didn't come in the house," Mr Swan told parliament in 2013.
The Speaker of the house, Anna Burke, asked the treasurer to withdraw the remark, describing it as a "very outrageous" comment. The treasurer complied with the request.
At the time, Mr Abbott responded by saying the treasurer was not being truthful.
"Wayne Swan should stop telling lies," Mr Abbott's spokesman said.
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'Not acceptable'
Prime Minister Malcolm Turnbull acknowledged his predesesor's error on Friday morning.
"It's clearly not acceptable or admirable in any way," Mr Turnbull told Neil Mitchell on 3AW radio on Friday.
"I can't remember anyone else missing a vote because they were too drunk to get into the chamber.
"But the fact is Tony has fessed up to it, he knows it was an error or whatever, he's acknowledged it and that's good."
Only human
When asked about the incident on Channel Seven's Sunrise program on Friday, former Victorian premier Jeff Kennett expressed surprise Mr Abbott was able to remember any details.
"All he's doing is showing that he's human," Mr Kennett said.
"And the beaut thing about politicians is they're fundamentally like all of us, they're human."
