Earlier in an interview with a local media outlet in Miami, Carter admitted that the USA soldiers "did stray accidentally into Iranian waters due to a navigation error".
Iran and the U.S. might have ended up in a "bloody war", had Washington followed Republican demand to confront Tehran over its detention of trespassing American sailors, says the White House.
Carter said the sailors were not on a covert mission and were simply making their way from Kuwait to Bahrain, both on the western coast of the Gulf.
"Our technical investigations showed the two US Navy boats entered Iranian territorial waters inadvertently", the IRGC said.
Two U.S. Navy boats were intercepted by Iranian forces after entering Iran's territorial waters.
CNN reported that many in the military "are alarmed by the silence, particularly from senior US military officials, including the defense secretary, at least saying that's wrong, you don't parade our soldiers and sailors on television like that".
The ten sailors were detained on Tuesday after their two vessels went off course near Farsi Island, where Iran's Revolutionary Guard Corps has a naval base.
Iran released footage Wednesday showing an American sailor apologizing for unintentionally crossing into Iranian waters along with nine others. Credit: Rexburgstandardjournal.com " After it became clear that the US combat vessels' illegal entry into the Islamic Republic of Iran's waters was the result of an unintentional action and a mistake and after they extended an apology, the decision was made to release them.
USA military officials said the video, which was posted online after the sailors' release, appeared authentic but claimed the apology was obviously staged.
He added that what has been depicted so far has been shown "through the lens of the Iranian media".
The U.S. Navy has initial statements from the sailors but is now conducting a full debrief, so additional information may come to light, the official said.
But it then became known the 10 sailors had been taken ashore and diplomatic efforts to get them out quickly kicked in.
Iran today released 10 United States sailors it had detained in the Gulf, moving within hours to head off a potential crisis as it prepares for the lifting of sanctions.
Bill Clinton, back on the trail, campaigns for Hillary
Carr also compared two past headlines about Trump's and Clinton's sex lives. Bernie Sander's remarks at the democratic primary debate in October.
