According to newly released government papers, the then UK prime minister only saw it was likely after getting "raw intelligence" two days before the Argentines landed.
The papers released under the 30-year rule show Thatcher was acutely worried about retaking the islands, 'BBC News' reported.
A historian said the documents were among the "most powerful material" declassified in the last three decades.
In October 1982, a few months after the war ended, Thatcher gave evidence behind closed doors to the Falkland Islands Review Committee, chaired by Lord Franks.
The transcript of that dramatic testimony has now been published for the first time, the report said.
"I never, never expected the Argentines to invade the Falklands head-on. It was such a stupid thing to do, as events happened, such a stupid thing even to contemplate doing", Thatcher told the Franks Committee.
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There had been some British contingency planning in the month before the Argentine invasion of the Falklands.
The then Ministry of Defence officials came back to Thatcher on March 26 1982 with a plan to deter a full-scale invasion.
One sentence shocked her, and she wrote it in her diary: "Moreover, if faced with Argentine occupation on arrival there would be no certainty that such a force would be able to retake the dependency".
"You can imagine that turned a knife in my heart, that lot," she told the committee.
In her oral evidence, however, she said she had still considered an invasion unlikely: "I again stress, I thought that they would be so absurd and ridiculous to invade the Falklands that I did not think it would happen.