Rachel Reeve's first budget as chancellor raised the National Insurance rate for employers from 13.8% to 15%, and lowered the salary threshold on which it is paid from £9,100 to £5,000.
That could have a particularly big financial impact for the Scottish government, which funds a proportionally larger public sector workforce than in the UK as a whole.
Mr Sarwar said the budget had delivered an extra £1.5bn for Scotland in the current financial year and £3.4bn more next year.
Pushed on the issue of National Insurance compensation, Sarwar said: "Which is why the conversation will happen between the Treasury and Scottish government.
"Something we committed to on the day of the budget and not something that's happened since the budget because we recognise there will be an impact for example on our national health service and that's not an impact we want to see."