But the First Minister also said the unintended consequence of her time in office was to drive Scots into backing Home Rule.
His initial official response to Mrs Thatcher's death was terse, saying only: "Margaret Thatcher was a truly formidable Prime Minister whose policies defined a political generation.
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"No doubt there will now be a renewed debate about the impact of that legacy.
"Today, however, the proper reaction should be respect and condolences to her family."
But Mr Salmond, in Washington DC as part of his visit to the US for Tartan Week, later added: "I didn't approve of her economic policies but I think it was the social policy dimension that created the level of opposition in Scotland."
He said her argument that there was no such thing as society was not a statement that would go down well with anyone in Scotland.
Mr Salmond also referred to the then Prime Minister's speech to the General Assembly of the Church of Scotland in 1988 – the so-called Sermon on the Mound – in which she offered a theological justification for her capitalist and market economics.
He said: "Famously in the Sermon on the Mound, when she developed that theme before the elders and brethren of the Church of Scotland, there was not the warmest reception that a Prime Minister could have received.
"I think the social policy dimension, almost a denial of society, was the thing that gave the opposition to her policies the most pointed nature in Scotland.
"The economic policies were disagreed with, but the social policies were antipathetic to the Scottish character, hence the degree and level of opposition that she provoked."
As a result, the First Minister claimed, she boosted demand for devolution.
He said: "Hence the unintended consequence that I think a lot of people in Scotland, looking at the poll tax, thought to themselves, well, the Scottish Parliament instead of just being a nice idea was something that was absolutely essential to prevent such a policy being imposed from on high again. That was an unintended consequence but a hugely important one."
However, Scottish Conservative leader Ruth Davidson called Mrs Thatcher a true Conservative revolutionary, challenging out-dated institutions, confronting vested interests and transforming Britain into a property-owning democracy.
Ms Davidson said: "She empowered millions of people in a way that was previously unimaginable and the positive impact of her legacy with be felt by thousands of families for decades to come.
"In becoming Britain's first woman Prime Minster and winning three consecutive elections she didn't so much smash the glass ceiling as blow it to pieces. She proved to women everywhere there was nothing they couldn't accomplish."
Ms Davidson said Baroness Thatcher would go down in history as one of the great Prime Ministers.
She said: "She defended Britain's sovereignty against opposition both at home and internationally and re-established Britain's reputation on the world stage, and the whole of the free world should be grateful for the crucial role she played in the downfall of Communism."
Her deputy Jackson Carlaw said: "I will never forget standing in front of the Grand Hotel in 1984 and being inspired as she strode onto the conference platform hours after the IRA bomb – her strength of character literally steeling the resolve of representatives and journalists alike."
One of the Iron Lady's contemporaries and greatest admirers, former Eastwood MP Allan Stewart, said: "She was a magnificent leader; clear-sighted and determined.
"For a period I was a Junior Minister, but it is as a constituency MP I remember her best. I went to see her about a factory closure in Barrhead. She was fully briefed and could not have been more helpful."
Scottish Labour Leader Johann Lamont said: "I came into politics to fight the ideology and values of Margaret Thatcher which I believe damaged our country. But today is not a day to debate that. Today is a day to offer the deepest condolences to her family, friends and all who loved her. No one can deny she made a deep mark on the history of this country."
Scottish Liberal Democrat leader Willie Rennie said: "Although I did not share her political outlook, as our first female Prime Minister she changed the face of our political system forever. While in many respects she was divisive, Margaret Thatcher was undoubtedly the leading political figure of her generation."
Former Liberal Democrat leader Sir Menzies Campbell said that although she would be best remembered for the Chruch of Scotland speech, Mrs Thatcher "had the courage to come and address the General Assembly with a critique of her own policy for which she claimed ethical justification. But as the reaction showed at the time she failed to impress the assembly or the Scottish public".
Iain McMillan of the Scottish CBI business group said: "Through sheer tenacity and immense courage, Margaret Thatcher changed the economy for the better and laid the ground for years of greatly improved economic performance."