A five-strong panel of judges in the UK’s highest court ruled on Wednesday that the Scottish Parliament needs Westminster approval to legislate for an independence vote.
Mr Robertson said the decision shows the UK is not a “voluntary union” after the judges ruled the Scotland Act does not permit Holyrood to legislate on the reserved issue.
Speaking at Holyrood on Wednesday, he quoted former Tory prime minister Margaret Thatcher who said “Scots have an undoubted right to self-determination” and that no politician or party “should stand in their way”.
He added that Scots “have chosen to have a choice but the Conservative Party, the Labour Party and the Liberal Democrats are working hand-in-glove to deny the people their say”.
Mr Robertson added: “We need democracy in this country. Today we have seen the end of the voluntary union as we know it.
“We will not give up on democracy in this country and people will have their say.”
His comments came as he faced an urgent question, led by Scottish Conservative leader Douglas Ross, on the Supreme Court ruling.
Mr Ross urged the Scottish Government to turn its focus on to NHS backlogs and the cost-of-living crisis.
He said: “We now have an opportunity, Cabinet Secretary, to focus on the big challenges Scotland faces right now.
“Strikes, the global cost-of-living crisis and a winter storm in our NHS.
“So can I ask the Cabinet Secretary, will the SNP Government ditch their obsession and get back to tackling these crucial issues for individuals, families and communities right across Scotland?”
He added that First Minister Nicola Sturgeon should have been in the Holyrood chamber to respond to the urgent question.
Mr Ross said: “Given the cost of this case in taxpayers’ money and time, I do think it’s regrettable that the First Minister herself was unable to come to this chamber to answer.
“She was more than happy this morning to comment from behind an SNP podium, as SNP leader, but she is now unwilling to answer questions today in this chamber from elected Scottish parliamentarians as First Minister.”
Mr Robertson said it is an “inconvenient truth” for Mr Ross that the Scottish Parliament election in 2021 gave the Scottish Government a mandate for a referendum.
Scottish Liberal Democrat leader Alex Cole-Hamilton said: “While Nicola Sturgeon goes through the motions, people wait days for an ambulance, months for NHS treatment and years for lifeline ferries.
“Breaking up the United Kingdom simply isn’t a priority for those people who are opening their bills with dread or living in pain.
“My goodness, teachers are on strike tomorrow. Scotland needs new hope, not old division.”