Mr Mackay confirmed that the Scottish government was considering a second independence referendum to keep Scotland in the EU.
He also told BBC Scotland a 9.5% budget deficit would not be an obstacle.
But the Scottish Conservatives said the SNP was "in denial" about the economic challenges facing Scotland.
And Scottish Labour said it was becoming "increasingly clear" that the promises made by the SNP ahead of the 2014 independence referendum were "completely misleading".
The EU stability and growth pact urges member states to keep deficits below 3% of gross domestic product (GDP).
Government figures for 2015/16 showed Scotland had a £14.8bn deficit when a geographic share of North Sea revenue was included, up from £14.3bn in 2014/15 .
This compares with an overall UK deficit of £75.3bn or 4% of GDP.
The UK's government's Scottish secretary, David Mundell, said the figures showed that being part of the UK protected Scottish living standards.
But Mr Mackay rejected the argument, saying "independence is one of the options that we are considering to secure Scotland's place" in the EU.
He insisted that Scotland's deficit was not a barrier to EU membership, arguing that the UK was running a deficit of more than 10% after the financial crisis.
The finance secretary told BBC Radio's Good Morning Scotland programme: "Take the financial year 2009/10. Coming out of the financial crisis, the UK deficit in terms of relative to GDP was over 10%.
"No-one suggested the UK was bankrupt then and would have to exit the EU."
The Scottish Conservatives said the minister's comments showed the SNP was "in denial" about the economic problems that would face an independent Scotland.
Finance spokesman Murdo Fraser said: "We were told the SNP was going to start being honest about the damage independence would cause to Scotland.
"Instead Derek Mackay showed this morning that the plan is still to shut their eyes as tight as possible in the hope everyone else does too.
"If ever an independent Scotland did seek EU membership, it would need to convince other EU nations that it had a plan to bear down on the huge deficit we're running. The last thing the EU would want is to take on the risk of another bail out.
"So Nicola Sturgeon needs to be straight with people - if she wants to make the case for independence within the EU, what would be the price of that be in higher taxes and reduced spending?"
Mr Mackay insisted that Scotland's large deficit showed that "UK economic policy isn't working for Scotland". and that an independent Scotland "would be able to make different choices and pull different economic levers to accelerate growth".
He also said the Scottish government had "put in place a £100m economic stimulus to support the economy, and that was new investment".
But Scottish Labour economy spokeswoman Jackie Baillie said: "The £100m Nicola Sturgeon announced was from a previous SNP government underspend, it's not new money - someone should have told the finance secretary.
"It's embarrassing that the man in charge of the accounts doesn't know where the money is coming from.
Ms Baillie said the Gers figures showed the "real benefits that Scotland gets from pooling and sharing of resources across the UK".
She added: "It is becoming increasingly clear that the promises the SNP made in 2014 were completely misleading, but rather than admit it, SNP ministers continue to spin utter fantasy to the Scottish people."
Scotland's large economic deficit would not disqualify the country from European Union membership, according to Finance Secretary Derek Mackay.