She recounted how she had to force herself to remain composed in front of TV cameras while inside she felt ready to cry while young Britons were dying 8,000 miles from Downing Street.
But after the agony, she said: "What the Falklands proved was that we could still do it, and do it superbly. There was a feeling of colossal pride, of relief, that we could still do the things for which we were renowned. And that feeling will stay with us for a very long time."
Although the sovereignty of the Falklands had been a simmering issue between London and Buenos Aires, Mrs Thatcher had no inkling that the landing of a few so-called scrap merchants on South Georgia in March 1982, and the running up of the Argentine flag there, would blow up into the greatest British campaign since the Second World War.
She declared: "If anyone had told me at the beginning that we should send 27,000 men and over 100 ships, I wouldn't have believed it."
On March 25, Argentine supply ships landed stores on South Georgia. This was airily dismissed at first by Downing Street, but it quickly became apparent that this was the forerunner to a full-scale military invasion of the Falkland Islands, known to Argentina as Las Malvinas.
A week later, Britain called an emergency meeting of the UN Security Council, warning that Argentina was about to invade the Falklands. And the following day, April 2, President Leopoldo Galtieri announced that his forces had landed on the islands and "reclaimed" them for Argentina.
The invasion brought with it the resignation of the then foreign secretary, Lord Carrington, and the declaration by the Prime Minister that Britain would recover the Falklands.
Private papers from 1982 released recently revealed wide divisions within the Conservative party over how the government should respond to Argentina's invasion of the Falklands.
While the Tories publicly presented a united front, briefing notes prepared for the prime minister demonstrate the polarised opinions she had to contend with in the early days of the crisis.
Ken Clarke told Margaret Thatcher Britain should just "blow up a few ships" over the Falkland Islands, while another Tory MP warned her his "constituents wanted blood", according to newly released files.
Meanwhile, the United Nations Security Council approved a British motion calling for the withdrawal of the invasion force and the opening of negotiations.
On April 5, Mrs Thatcher ordered a taskforce to sail for the Falklands to undertake what military experts feared was a dangerous gamble - fighting a war 8,000 miles from home.
It was the biggest UK naval operation since the Second World War. Within two months, on May 21, the first British troops were wading ashore on one of the rocky beaches, and on June 14, Argentine troops surrendered at Port Stanley.
But within that period, 1,000 men were killed, including more than 400 in the Argentine warship the Belgrano, a sinking which has remained a hotbed of controversy ever since.
Those who attack the decision to sink the vessel on May 3 say she was leaving the exclusion zone around the islands, but Mrs Thatcher vehemently maintained that the Belgrano was a threat to the British taskforce.
There were moments of deep sadness and grief with the sinking of HMS Sheffield and HMS Antelope and the attacks on HMS Glamorgan and other British ships.
But there were also moments of elation, for instance her cry of "Rejoice!" when South Georgia was recaptured.
Throughout the conflict, Mrs Thatcher wore black. She constantly spoke of "our boys". It was for her, more than anyone else except those fighting the war, 74 days of trauma.
"Everyone was at risk," she said. "We were always worried about the vulnerability of the supply lines especially.
"The Argentine aircraft carrier had only to come out. She was in easy reach of our supply lines. We were desperately worried about the Canberra.
"You can imagine the agony. How could they miss the Canberra? One lived with the agony of the soldiers in the troop ships."
But the war changed her. "It puts other worries in perspective - and always will," she said. "It makes you very impatient when people magnify small worries into big ones.
"When it was all over there was a tremendous sense of relief. A feeling that whatever problems I have to go through now, at least I won't have to go through that terrible period when every time the phone rings, every time the door opens, you worry."
The following January, Mrs Thatcher visited the Falklands. She was greeted like a saint by the Falklanders as their saviour.