The fictional look at the creation of Facebook dominated at the society's annual awards, which were voted on by 46 prominent movie critics gathered at a Manhattan restaurant.
Jesse Eisenberg was named best actor for his role as Mark Zuckerberg, the founder of the social networking website. David Fincher won for best director and Aaron Sorkin for best screenplay.
The critics reached overseas for the best actress honor, naming Italian star Giovanna Mezzogiorno for her role in "Vincere." The film follows the rise to power of Italian dictator Benito Mussolini, with him abandoning his wife and child along the way.
Supporting actor awards went to Geoffrey Rush for "The King's Speech" and Olivia Williams for "The Ghost Writer."
The society, founded in 1966, is composed of 61 film critics from across the country, including Roger Ebert of the Chicago Sun-Times, the Los Angeles Times' Kenneth Turan, The Wall Street Journal's Joe Morgenstern and David Denby of The New Yorker.
While these critics' choices rarely reflect top honors at the Academy Awards, the New York-based society helps draw attention to new films in advance of the Oscars, staged in late February by the Academy of Motion Picture Arts and Sciences.
On Saturday, society members issued a statement calling for a re-examination of the movie rating system set by the Motion Picture Association of America.
The critics praised a decision to change the NC-17 rating for "Blue Valentine" to an R, but they questioned others. They singled out "The King's Speech," a drama about King George VI's attempt to overcome his speech impediment, which was rated R for "language" - moments when he's told to swear to ease his stammer.
"It's clear the board has become an agency of de facto censorship," read the statement from the critics, who suggested a revision of the current system.
The society also condemned Iran's recent sentencing of directors Jafar Panahi and Mohammad Rasoulof to six years in prison. Both were banned from filmmaking for 20 years for "colluding in gatherings and making propaganda against the regime."
The critics urged the Iranian government to release the directors, saying their "work can only further the advancement of such values as justice, compassion, tolerance, and human dignity."
Among foreign language films, "Carlos" - French director Olivier Assayas's 5 1/2-hour-look at the life of the global terrorist dubbed "Carlos the Jackal" - was voted best.