A draft statement that mentioned Ban's support for the LGBT community was changed to note instead that "the most vulnerable or marginalised have been increasingly heard and assisted" under his leadership.
Ban, the 72-year-old former South Korean foreign minister, steps down on December 31 after serving two terms as secretary-general of the United Nations.
He will be succeeded by Antonio Guterres, the former prime minister of Portugal who served as UN refugee chief for a decade. Ban has won praise from LGBT activists for his appeals to countries to decriminalize homosexuality.
The outgoing UN chief came under fire from many UN member-states including Russia when he decided in 2015 to extend benefits to the same-sex partners of UN employees.
In September, he hosted the first high-level meeting at the United Nations on the rights of lesbian, gay, bisexual and transgender people to push for an end to discrimination.
More than 70 countries still have laws on their books making homosexuality a crime. The statement read by Spanish Ambassador Roman Oyarzun, who holds the council presidency this month, listed the Paris climate deal and the UN's new sustainable development goals as Ban's major achievements.
Addressing the council, Ban said his "deepest regret on leaving office is the continuing nightmare in Syria."
He again appealed to the council to unite and take action to protect Syrian civilians as the city of Aleppo came under renewed shelling and air strikes in one of the fiercest battles of the five-year war.