Annan, who has been under pressure over scandals including the Iraq scheme, acknowledged "there have been mistakes in the oil-for-food thing. Serious allegations have been made ... we are taking measures to strengthen our own administration and transparency".
"I hope that the member states, who are focused on the reform initiative, will continue on that," Annan said on Friday.
"I do not expect it to derail the reform process."
The UN chief has presented an ambitious UN reform project - including expanding the UN Security Council - which he hopes to see passed at a summit of world leaders in September.
Annan said UN members, who knew how oil-for-food was set up and managed, "are much more sanguine about the facts than most other people, and I hope they will focus on the work and strengthen this institution".
"For some, the oil-for-food crisis will never die down," he said.
The $64 billion oil-for-food programme, which ran from December 1996 to November 2003, was intended to ease the effects of international sanctions on ordinary Iraqis, allowing Iraq to sell oil and use the revenue to buy humanitarian supplies.