Thatcher was angered by the US leader's decision to invade part of the Commonwealth without consulting her.
A recording of the conversation between Reagan and Thatcher following the invasion of Grenada has been made public for the first time, BBC reported.
United States troops were sent to Grenada in 1983 to topple the Caribbean island's Marxist regime.
While US forces were still in action, the then US President phoned Thatcher to apologise for the breach of protocol.
The saying refers to an Civil War-era practice in which a visitor might throw his hat in to a room before entering -- if he was unwelcome, it might be thrown out again or even shot.
"There's no need for that," Thatcher replied.
Reagan said: "We regret very much the embarrassment that's been caused to you, and I would like to tell you what the story is from our end."
He explained that military commanders only had "a matter of hours" to mobilise the troops and that he was prevented from discussing it with her sooner because of security fears.
Thatcher went on to suggest she understood why he had not been more open with her, saying she had been subject to similar restrictions at the time of the Falklands invasion.
"The action (in Grenada) is under way now and we just hope it will be successful. There is a lot of work to do yet, Ron," she said.
The pair discussed the situation in Grenada further before she ended the call by saying she had to return to a "tricky" debate in the House of Commons.
A box of 20 tapes was released to the public in October at the Reagan Library in Los Angeles, following several Freedom of Information Act requests.
The release confirms that President Reagan secretly recorded his discussions in the White House situation room, a habit that was previously thought to have ended with Richard Nixon's departure from office.
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