"I don't know what happened in that meeting," Coats told NBC News' Andrea Mitchell at the Aspen Security Forum in Colorado.
Trump met Putin for more than an hour, with just their interpreters in the room, on Monday.
Coats, the director of national intelligence, said he would have opposed that arrangement, which left Trump without an official stenographer or aides in the room.
"If he had asked me how that ought to be conducted, I would have suggested a different way, but that's not my role," Coats said. "It is what it is."
During Coats' interview, White House press secretary Sarah Huckabee Sanders announced in a tweet that Trump had asked National Security Advisor John Bolton to invite Putin to the White House in the fall.
Coats' real-time reaction to the news drew a laugh from the crowd. "Say that again?" he asked.
"Okay," he said after a pause. "That's gonna be special."
Trump's aides were concerned that Coats' remarks in Aspen would enrage Trump, according to The Washington Post.
“Coats has gone rogue,” the paper cited a senior White House official as saying.