The industry had described plans for a 10% rise in duty from August this year as a "historic blow".
First Minister Humza Yousaf raised their concerns with Mr Sunak when they met in London on Monday.
The prime minister has told the BBC that "the chancellor makes all tax decisions and that decision has been made".
He claimed the UK government was a "big supporter" of the whisky industry, freezing duty in nine out of the last ten budgets.
Scottish Secretary Alister Jack made clear that he had lobbied against this year's tax rise.
In 2019, the Conservative manifesto promised to "review alcohol duty to ensure that our tax system is supporting British drink producers".
Mr Sunak said the industry was also concerned about the potential "damaging impact" of the Scottish government's proposed deposit return scheme.
He said he was "glad" ministers in Edinburgh had decided to pause and reconsider their plans.
Asked if he was minded to grant an exemption from UK internal market rules to allow the scheme to go ahead in March 2024, he said the request would be considered in a "rigorous and objective way".
Earlier this week, the SNP's Westminster leader Stephen Flynn accused the UK government of using its powers to threaten devolution.
He cited the use of the internal market act and the section 35 order that has blocked Holyrood's gender recognition reforms from becoming law.
The former chief Brexit negotiator Lord Frost - a Conservative peer - has called for devolved powers to be reviewed and rolled back.
The prime minister said he had not seen Lord Frost's specific comments but he said "in general, I don't think we should be rolling back devolution".
On the gender reform intervention, he said the UK government would "robustly defend" its position in court against the Scottish government's challenge.
Mr Sunak also rejected the idea floated by Scottish Conservative leader Douglas Ross that Tory voters might get behind candidates from other parties if they are better placed to defeat the SNP.
The prime minister said Mr Ross was acknowledging that tactical voting may happen in local areas but stressed that his view is that "Conservatives should vote Conservative".
The Scottish Conservatives are gathering in Glasgow this weekend for their spring conference.