Haruki Wada, who headed the fund, said the results had been "rather ambiguous, but it was the best we could do at that time".
"As far as Japan's reconciliation with Asian neighbours is concerned, our achievement was insufficient," he said.
The Asian Women's Fund was established in 1995 to aid former "comfort women", women who had been forced into prostitution by Japan's military during World War II.
It provided 285 women in the Philippines, South Korea and Taiwan with two million yen ($17,800) each in compensation, helped set up nursing homes for former "comfort women" in Indonesia and offered medical assistance to some 80 former Dutch sex slaves.
But many victims rejected the aid because it neither came directly from the Japanese government nor was accompanied by an official government apology.
The fund came to an end on Saturday with the termination of a nursing home programme in Indonesia, the fund's final project.
Shinzo Abe, Japan's prime minister, recently provoked outcry on the issue of "comfort women" by suggesting there was no proof that Japan's Imperial government or military coerced women into prostitution.
On Monday, Abe tried to quell the backlash, saying: "I express my sympathy toward the 'comfort women' and apologise for the situation they found themselves in."
But Abe has stopped short of acknowledging Tokyo's role in Japan's wartime conscription of "comfort women".
Meanwhile, at talks on Saturday on the South Korean island of Jeju, Taro Aso, Japan's foreign minister, sought to reassure Song Min-soon, the South Korean foreign minister, that Abe did stand by an earlier apology issued by Japan in 1993.
Mitsuo Sakaba, a Japanese foreign ministry spokesman, said that Song "appreciated" the clarification, but urged Japanese political leaders to be "careful not to create any doubt about the Japanese position on this particular matter".
Some historians have said that as many as 200,000 women, mostly from the Korean peninsula and China, served in Japanese military brothels throughout Asia in the 1930s and 1940s.
Many victims say they were kidnapped and forced into sexual slavery by Japanese troops.
After decades of denial, the Japanese government acknowledged its role in wartime prostitution after a historian unearthed documents indicating government involvement.