The 12 Years a Slave director took to the stage in tears after a moving introduction by Harry Belafonte at the 69th annual ceremony, held at the Edison Hotel Ballroom in Gotham.
However, Critics Circle member Armond White - controversial film critic for CityArts - yelled at the filmmaker, who won the Best Director prize.
"You're an embarrassing doorman and garbage man. F**k you. Kiss my ass," White is quoted as saying by Variety.
White is known to have behaved similarly at past ceremonies, and has been a negative critic of 12 Years a Slave since October. However, his remarks were not heard at the front of the room and did not interrupt the ceremony.
Elsewhere, American Hustle won awards for Best Picture, Best Supporting Actress for Jennifer Lawrence and Best Screenplay.
Robert Redford won Best Actor for All Is Lost, while Cate Blanchett was named Best Actress for Blue Jasmine. Jared Leto won Best Supporting Actor for Dallas Buyers Club.
Bradley Cooper accepted co-star Lawrence's award on her behalf, who had sent a message joking she was not receiving it for 2012 movie The House at the End of the Street.
Blanchett said of her award: "Thank you to the New York Film Critics Circle for showing such great taste and discernment in giving me this award."
Glenn Close presented the award to Redford, who received a standing ovation from the audience. Paraphrasing TS Eliot, he said: "What we call the beginning is often the end. And to make an end is to make a beginning. The end is where we start from."
Harry Belafonte spoke of how cinema has depicted black people during his life, from The Birth of a Nation to Tarzan. He said: "Now, I can say, in my 87th year of life, I am overjoyed to have seen Steve McQueen step into this space and give us a film that touches the depths of who we are as a people."
Watch a trailer for 12 Years a Slave below: