Mr Abbott has revealed he failed to make a key vote in 2009, while a shadow minister, after drinking too much wine the night before.
Rumours had swirled over why Mr Abbott missed the vote on a stimulus bill during the global financial crisis.
Mr Turnbull, then opposition leader, described the incident as unacceptable.
"There was nothing we could do," Mr Turnbull told radio station 3AW on Friday.
"As Tony acknowledged, the whips [fellow MPs] tried to rouse him to get him down into the chamber to vote, but they were unable to move him."
Mr Turnbull said Mr Abbott's absence was "not acceptable or admirable in any way" and the vote had been important.
"I was disappointed. I cannot remember anyone else missing a vote because they were too drunk to get into the chamber, but the fact is that Tony has 'fessed up to it, he knows it was an error or whatever," Mr Turnbull said.
Mr Abbott toppled Mr Turnbull for the Liberal Party leadership later in 2009, only for Mr Turnbull to reclaim it in 2015, when Mr Abbott was prime minister.
Mr Abbott remains a vocal critic of the government and is opposed to gay marriage, a position which has put him at odds with the prime minister.