He spoke to the press when it would have been better for him to keep quiet, he said on Newsmax TV's "Steve Malzberg Show."
"I screwed that one up," Richardson said.
"I thought we had a deal. I went in and talked to the Cubans. The Cubans were changing their policy at the last minute.
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"Instead of shutting up and waiting for things to calm down, I was in Havana and I went to the press. I said 'Alan Gross is a political prisoner, [and] the Cubans are not playing straight.'"
Richardson, Bill Clinton's U.N. ambassador from 1997-98 and later energy secretary and governor of New Mexico, is the author of a new book, "How to Sweet-Talk a Shark: Strategies and Stories from a Master Negotiator."
The book, he said, points out his successes, but in Gross's case, he admits he made a mistake.
"The Cubans just dropped me off and I just wasn't able to get Alan out."
Richardson says he learned an important lesson: "Sometimes you can't go public, you can't show your emotion," Richardson told Malzberg. "You've got to be very restrained and careful when you're negotiating."
And, he said, he'll "always regret" going the press over Gross, rather than remaining quiet, "even though there have been many others trying to get Alan out."
He said he feels "a lot for [his wife] Judy Gross. I met her, I talked to her. I mean, her husband has been unfairly incarcerated, but I wish I hadn't lost my cool."
At the time, Richardson said, he had not "been in negotiation in a while, and I was no longer governor, so I kind of lost my power base."
Gross, 64, was working in Cuba as a subcontractor for the U.S. Agency for International Development when he was arrested on Dec. 3, 2009, and charged with "actions against the independence or the territorial integrity of the state.”
The Cuban government accused Gross of spying for carrying telecommunications equipment to the island and sentenced him to 15 years in prison. According to Gross, he was contracted by Development Alternatives Inc., as part of a contract with USAID, to establish wireless networks and Internet connections for non-dissident Cuban Jewish communities.
Cuba state prosecutors, though, accused him of performing a “subversive project aiming at bringing down the revolution” by disseminating distorted information about the government.
Gross wrote a personal letter to President Barack Obama on Tuesday, the fourth anniversary of his imprisonment.
Judy Gross told Malzberg on Wednesday that her husband feels "abandoned" by the United States.
"My hope is that the government is able to sit down and start talks and negotiate with the Cuban government," she told Malzberg. "That's how you start getting things done. You have to sit down sometime and start dialogue."