"Mr McCully told the programme he accepted he was critical of the Security Council in his recent speech.
Three weeks ago Mr McCully addressed the United Nations General Assembly, in a bid to secure New Zealand a place on the United Nations Security Council.
In his speech Mr McCully said he believed the problems of the Middle East were "deep and difficult" and said the UN must fundamentally improve its performance in preventing conflict.
"In Syria and Iraq we see the truly frightening consequences when leadership, both internally and in the Security Council, has failed," Mr McCully said in his speech.
Mr McCully told The Nation that the sentiments he was expressing in his speech, were in line with the mood of many countries. "I think a lot of countries voted for us identifying with those criticisms and hoping that we would at least make an honest attempt to improve things," he told The Nation.
"I don't think there is one silver bullet here, I think there are lots of small things that need to be done to improve the way the Security Council works."