The armory is being used for current Fashion Week events.
Cuomo said the public had the right to pay a fair price for using a state space, which the armory is, and should not accept any attempts at extorting more money.
"You pay the fair value for that space," he said. "What you don't pay is a gratuity or a bribe or an illegal tip to get you into that space."
Jackson, who resigned from his post shortly after his arrest in October, pleaded not guilty at his arraignment. His attorney, Alan Abramson, declined to comment.
If convicted, Jackson, 56, could face more than 20 years in prison.
The indictment charged Jackson with taking bribes in connection to Marc Jacobs shows from February 2000 to September 2007 and other trade shows in 2007 and with defrauding the government. Cuomo said Jackson received more than $30,000.
Cuomo said the bribes for the fashion shows were paid by KCD, a public relations company that the fashion house used. Neither KCD nor Marc Jacobs was named in the indictment.
The investigation was continuing, though, and Cuomo said the payment of bribes could be a crime depending on the circumstances.
KCD attorney Ken Breen said the company was cooperating with Cuomo's investigation.
In a statement, a Marc Jacobs representative said the fashion house, which is using the armory for shows this Fashion Week, was aware of the charges against the armory superintendent and was cooperating with the state attorney general's office in its investigation.
"We are using the armory for this week's fashion shows with the full knowledge and consent of the attorney general's office," the statement said.
The 69th Regiment Armory, which occupies much of a Manhattan block at 25th Street and Lexington Avenue, was built to serve as a training center and social clubhouse for the National Guard. It was entered into the State and National Register of Historic Places in 1994 and was listed as a National Historic Landmark two years later.
