The UN chief's annual report on the work of the body refers to its experience in Sri Lanka handling the humanitarian crisis.
"I have engaged the organisation in a reflection on strengthening our own capacity to respond to crisis situations and protect human rights through follow up to the internal review panel on UN action in Sri Lanka," Moon said.
In 2011, the UN had appointed a special panel to review its Sri Lanka operations during the final phase of the military campaign against Tamil rebels LTTE.
As many as 40,000 people were reportedly killed in the last months of the nearly three decade long conflict between Sri Lankan troops and the LTTE fighting for an independent homeland.
The UN panel report has accused both the government and the Tamil rebels of wrongdoing during the war that ended in 2009.
Sri Lanka slammed the report as baseless, biased and unilateral.