Barrera spoke through an interpreter at his court appearance, Voice of America reported. He is being held without bail.
The hearing came a day after Barrera's arrival in the United States, The New York Times said. He was arrested in Venezuela, extradited to Colombia and then extradited again.
Barrera is scheduled to appear Thursday in federal court in Brooklyn.
His arrest last year followed an investigation involving both Venezuelan and Colombian agencies, British and U.S. intelligence and the U.S. Drug Enforcement Administration.
Barrera, nicknamed "El Local," allegedly made tens of millions of dollars from cocaine trafficking. Investigators say he bought raw cocaine past from the Revolutionary Armed Forces of Colombia, the guerrilla group known by the acronym FARC, and then processed it.
The president of Colombia has called him "the last of the great kingpins."