In the audio released by the New York Times, Kerry is heard lamenting to a group of Syrian civilians last week in New York that his call for US action against Bashar al-Assad's government fell on deaf ears.
"I think you're looking at three people, four people in the administration who have all argued for use of force, and I lost the argument," he tells the group.
"I've argued for the use of force ... but things evolved into a different process."
State Department spokesman John Kirby did not deny that the recording -- made at a private meeting in a diplomatic mission on the sidelines of the UN General Assembly -- is authentic.
"While we will decline to comment on a private conversation, Secretary Kerry was grateful for the chance to meet with this group of Syrians, to hear their concerns first hand and to express our continued focus on ending this civil war," he said.
It has been widely reported that Kerry pushed President Barack Obama to take a more robust path in Syria, to give teeth to international efforts to force Assad aside and end a civil war now heading into its sixth year.
But Washington's top diplomat has been careful to present a united front with the White House in public, even as he attempts to work with Moscow to rein in Assad's forces and build space for a political dialogue.
Signup to our newsletter and follow us on Facebook and Twitter!
In August 2013, after Assad had been accused of firing chemical weapons at civilians, Kerry gave a ferocious speech that was seen as prefiguring a retaliatory US military strike -- only for Obama to back down only hours later.
Kerry refers to the speech incident in Friday's leaked recording, but blames the US Congress for refusing to vote to authorize the US military to take action against Assad.
At last week's meeting, the Syrians -- sympathizers with the rebellion against Assad -- expressed frustration that US efforts in their country are focused on fighting the Islamic State group and not on Assad or his allies.
Instead, on September 9, Kerry agreed with Assad's ally Moscow that there should be a ceasefire between the regime and the US-backed rebels. The truce came into force on September 12 but fell apart after a week.
Russia and the United States are now blaming each other for the breakdown and Assad's Russian-backed forces have launched an assault on rebel-held eastern Aleppo.
"Look, I get it," Kerry tells the incredulous Syrians.
"A lot of us wish there was an enforcement mechanism right now. A lot of us have been fighting for one, but we don't have one right now and that's set," he warned.
"We're trying to pursue the diplomacy, and I understand it's frustrating. You have nobody more frustrated than we are."