The world body has never had a female leader in its 70 years. With Ban Ki-moon, the current incumbent, set to step down at the end of the year, Malcorra leads a pack of five women candidates seeking to change that.
But she told Argentine newspaper Clarin that "there is still a biased vote against women" at the UN.
"Given equal abilities, there is always a small negative margin against women," she said.
In the UN's most recent secret straw poll leading up to the election, Malcorra came in third place, behind Portugal's former prime minister Antonio Guterres and Serbia's former foreign minister Vuk Jeremic.
She said she was "very satisfied on a personal level" with the August 5 vote.
But she added: "Unfortunately, in general terms, women candidates do much worse than the men. That pains me, because it seems to me I have very distinguished women colleagues with a lot of experience."
She was named Argentine foreign minister when conservative President Mauricio Macri took office last December.
The 15-member Security Council has so far held two straw polls to whittle down the field of 11 candidates for secretary-general. More are expected in the coming weeks.
Members are facing calls to pick the first woman after eight men in the job, and to give preference to a candidate from Eastern Europe, a region that has yet to be represented in the post.
Council diplomats are expecting a nominee to emerge in October, who will then be endorsed by the General Assembly.
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