The SNP leader was speaking to thousands of Yes supporters outside Holyrood at a rally organised by Believe in Scotland and Yes for EU, who claimed a crowd of 25,000.
However the First Minister was also heckled during his 15-minute speech as he spoke about independence, with a man in the crowd shouting: “How do we get there?”
Mr Yousaf said independence was “not a sideshow” but a fundamental ingredient in the success of a host of European nations of similar size to Scotland.
He said: “If it works for them, with all the talent and resources and wealth that we have, then why not Scotland? Why not our nation?
“We stand here in front of our nation’s parliament. Why? We stand here to rededicate ourselves to that cause, independence.
“My God, the people of our country need it now, more than they have ever needed it.
“We believe in independence because this unequal Union has caused so much suffering and so much harm.
“Let me tell you, the people of this country are not suffering from a cost-of-living crisis, they’re suffering from a cost of the Union crisis.”
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He added: “Our job is to inspire, not just point out the failings of a miserable Westminster government but to inspire people, give them a reason to vote for independence.”
Speaking to the media later, Mr Yousaf was asked what he meant by the cost of the Union and said: “All the suffering that people are having to endure at the moment, the cost of living crisis, high energy bills, whether it’s any impact of austerity over the past 13 years, we have to remind people that independence is the answer.
“It’s the antidote to that.
“If we had powers in our own hands we wouldn’t have cruel Westminster policies foisted upon us. So that’s the message – independence is absolutely linked to the cost of living crisis, or austerity or the fact that our economy has suffered because of Brexit.”
Asked if he could be the First Minister who delivers independence, Mr Yousaf said: “That’s certainly the aim. Certainly the hope. There’s not a shortcut to independence.
“We know that, we understand that. The UK Government and UK parties continue to deny the democratic mandate that we have.
“We’ve got to create the conditions to make it impossible for them to ignore. The only way we do that is by mobilising the power of the people.”
Asked about the heckler’s question, how do we get there, he said “Plan A” continued to be to demand a referendum by mobilising the power of the people, and the next opportunity to test that would be through the general election.
He has previously recommended judging success by the number of MPs won, but the SNP is set to decide on a concrete method at its conference next month.
SNP independence minister Jamie Hepburn and Scottish Green minister Lorna Slater also spoke at the 90-minute event, which was preceded by a march from Edinburgh Castle.
The Scottish Greens co-leader said: “Every day when I’m at work I am asking: ‘What we can do to make things fairer, how we can make sure more people get a living wage, how we can do more for the climate?’
“And I’m told: ‘We can’t do that, those powers are not devolved.’
“And that’s before Westminster began rolling back the powers that our Parliament has and disrespecting this Scottish Parliament.
“They’re pushing back on the work we are doing for equalities and for our environment, things we believe in deeply and that we know matter to the people of Scotland.”
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Tory MSP Donald Cameron said: “Humza Yousaf needs to realise he is the First Minister for Scotland, not the SNP, and his appearance at the independence rally shows his top priority is to push for another divisive referendum.
“People across Scotland will be infuriated that the First Minister attended this march and believes separating our country is more important than helping households through the global cost-of-living crisis and fixing our broken NHS and crumbling schools.
“Humza Yousaf continues to be completely out-of-touch with public opinion and people are rightly seeing through his reckless behaviour.”