Last week, Mr Kwarteng announced a series of measures including plans to scrap the top rate of income tax and cut the basic rate to drive economic growth.
The pound tumbled to its lowest-ever record against the US dollar following the announcement and the International Monetary Fund (IMF) condemned the proposals.
The Bank of England launched an emergency government bond-buying programme to prevent borrowing costs from spiralling out of control and stave off a “material risk to UK financial stability”.
Speaking to journalists in Holyrood on Thursday, Mr Ross was asked how worried he is that people will be worse off because of the market reaction.
He said: “Well, it's an absolutely huge concern. I'm a mortgage payer, like the vast majority of people here in Scotland and across the UK. That's a considerable concern.
“I think it is right that in terms of tax reductions that we see as many people, from lower earners through the tax system, paying less tax so they have more of their own money to spend in local economies, supporting local businesses.
“But that is being offset at the moment by, as we see, the increasing interest charges, and people are struggling and we've got to do everything we can to support them, support businesses.”
He said the “biggest single element” of the mini-budget was the announcement of more than £60 billion in energy bills support.
Mr Ross said the Chancellor would “reassure the markets that there is a long-term plan to get this under control” when he sets out his medium-term fiscal plan in November.
He said Rishi Sunak, the former chancellor who went up against Ms Truss in the battle for No 10, “predicted a lot of what has happened".
The Scottish Tory leader said: “I think Rishi has not said much in the last week. But clearly there was a difference of opinion between Rishi and Liz over the course of the entire election campaign and the members supported Liz and she's taken forward her plans as Prime Minister.
“But I reiterate, clearly, there has to be a reaction to what has happened with the markets and the intervention from the Bank of England yesterday, and the Chancellor has confirmed that he is constantly engaging with the Bank of England to look at what more we can do to support.”
Mr Ross said he had "not said to anyone" who he voted for in the Tory leadership race.
Asked if he had confidence in Mr Kwarteng and Ms Truss, he said: “Yes, I have confidence that the Chancellor and the Prime Minister are doing everything they can to respond to the reaction that we've seen from the Bank of England and the markets.”
He said there were “significant elements of the budget that are very good for Scotland and the whole United Kingdom”.
Put to him that the tax cuts had caused the current problems, Mr Ross said: “Well, you know, we've got to look at the global situation as well.
“I mean, we've seen currencies across the globe fall, and I was just looking at that in the [Holyrood] chamber before I came out here – the incredible strength of the dollar is also having an impact across Europe, and in other currencies across the globe.
“As I say, the Government are not ignoring the response from the markets.”
Mr Ross later said: “I want to give the Chancellor and the Prime Minister and the whole Government the opportunity to get out there to ensure that we provide the answers that the market are looking for, but crucially, the public and business owners, homeowners etc, who are worried right now.”