But he also said he had taken a large amount of cold medicine.
At Sunday's news conference alongside Masaaki Shirakawa, the Bank of Japan governor, Nakagawa's speech sounded slurred.
At one point, Nakagawa, his head down and eyes closed, mistook a question directed at the bank governor as one for him.
Announcing his departure on Tuesday Shoichi Nakagawa told reporters that Aso had asked him to stay in his post, but analysts say opposition parties had pressed for the minister's resignation.
"It is a fact that I didn't conduct myself clearly, and I feel I must put it straight," Nakagawa told reporters in Tokyo about the news conference in Rome.
The scandal over Nakagawa's behaviour comes as Aso's public support is plummeting ahead of an election that must be held no later than October, and as the economy sinks deeper into recession.
One poll published on Sunday showed his approval rating below 10 per cent.
Nakagawa said his performance had not harmed Japan's standing or its relations with G7 nations, but the main opposition Democratic Party said he should lose his job.
"His responsibility for having shown disgrace to the world is heavy. I think this is an embarrassment," Ichiro Ozawa, the leader of the Democratic Party, told the Associated Press.