Since he announced his tax plans, UK Chancellor George Osborne introduced a new system for the rest of the UK.
It resulted in properties at the higher end of the market attracting a lower rate of tax than the proposed Scottish system.
The changes in Scotland are due to come into effect in April.
Mr Swinney’s initial plans raised the threshold for paying tax on a home from £125,000 under stamp duty to £135,000, with rates ranging from 2% up to 12% on the portion of any price above £1m.
Earlier this week, Mr Swinney told BBC Scotland: “I did not intend to raise more tax than the tax I was replacing or to cut tax.
“The consequence of the Chancellor’s announcement in December is the amount of tax that he intends to raise from this has reduced quite significantly.
“So, if I want to remain true to my principle of this change being revenue neutral – that it doesn’t increase or lower the taxes that are generated – then the right thing to do is to look at these issues.”
Much of the criticism from Mr Swinney’s political opponents has focussed on the 10% rate being levied on properties costing more than £250,000.
Conservative finance spokesman Gavin Brown said: “The eye-watering 10% tax rate has caused concern in many parts of Scotland and is having a distortion on the housing market.
“There is a clear and obvious way to fix this distortion – the Scottish government can use the windfall from UK stamp duty changes to create more realistic tax rates with a shallower increase.”