"The outcome is sufficiently encouraging to stay very focused on this," she said.
Asked if she had some threshold in mind which would force her out of the contest, she said: "I don't have any plan B scenario on that, no. You just take each phase at a time and just calibrate around that."
She praised her former political foes, Key and McCully, saying they had worked extremely hard.
"I couldn't have asked for more from John Key or Murray or the diplomatic service or indeed the New Zealand public. They've been absolutely fantastic."
Clark was Prime Minister for nine years before Key and has been administrator of the UN Development Programme for seven, which was what took her to Cameroon.
She told the Herald that she remained a strong and serious candidate and said the final outcome would be the result of a negotiation.
Without exception, wherever Key, McCully, herself and New Zealand diplomats went, she was regarded by other countries as a strong and serious candidate.
It is my view ... given New Zealand's position in the world, and my own track record, that we can be that candidate.
"So the issue is going to be whether the geo-politics enable this strong and serious candidate to make it through.
"Absolutely no one is getting push-back [from countries] saying 'what on earth is New Zealand on about?' No, they are saying this is a very serious candidate."
She was staying in the contest because in the end, there would be a negotiation and someone had to come through that negotiation.
"And it is my view that a strong New Zealand candidate, given New Zealand's position in the world, and my own track record, that we can be that candidate."
Despite a strong push for an Eastern European and/or a woman to get the job, former Portuguese Prime Minister Antonio Guterres topped the ballot again in the Security Council's third indicative ballot.
He received 11 "encourage" votes, three "discourage" and one "no opinion".
Clark received six "encourage", eight "discourage", and one "no opinion".
The last two, Christiana Figueres of Costa Rica and Natalia Gherman of Moldova, each received only two votes of "encourage", 12 of "discourage" and one "no opinion". Two candidates had already dropped out and they are likely to be the next two.
There is still volatility in the votes for Eastern Europeans with Slovakian Foreign Minister Miroslav Lajcak rocketing up from 10th to second and Slovenian Danilo Turk diving from fourth to eighth.
Two women polled higher than Clark - Irina Bokova of Bulgaria and Susana Malcorra of Argentina, but being respective favourites of Russia and the United States, they may well attract vetoes.
It is not known when the next poll will be but it has been widely expected that there won't be a result until October at the earliest.
The Security Council must make a recommendation for the General Assembly to approve before Ban Ki-moon's term expires at the end of the year.