The reform, which would see the top rate of tax scrapped and the basic rate cut to 19p in the pound, spooked the financial markets, sending the pound to its lowest level against the US dollar.
Sterling rebounded to $1.12 on Friday morning – just shy of the $1.13 seen before the announcement.
Scottish Secretary Alister Jack said the announcement of tax cuts should not have come as a shock.
Throughout the Tory leadership race, Ms Truss was adamant that a government she leads would cut taxes – though she did not go into detail about the level of cuts.
Speaking to BBC Radio Scotland on Friday, Mr Jack said: “When you say ‘huge shock’, over the summer [Ms Truss] was very clear that her strategy was to reduce taxes.
“She and [leadership rival] Rishi Sunak argued that out over the summer. He said one thing, she said the other, but it shouldn’t come as a shock to anyone when she said she believed the strategy was to be more of an Asian tiger economy, where you keep your higher spending, but you grow your economy, and she said to do that she would be cutting taxes.
“To anyone paying any attention to that leadership contest, it was plain as day what was going to happen.”
Mr Jack went on to say that due to the invasion of Ukraine, the UK Government had to step in to help households deal with their energy bills, which “has been inflationary”.
The Prime Minister and Chancellor are meeting with the Office for Budget Responsibility (OBR) on Friday, after criticism that an updated forecast was not published alongside the so-called mini-budget last week.
Mr Jack said the Government had to act quickly to deal with rising energy bills and could not wait for an OBR update, which he said could take between eight and 12 weeks.
The Scottish Secretary – reappointed to his post by Ms Truss after serving under her predecessor Boris Johnson – was also unmoved by recent polling showing a large Labour lead.
A YouGov poll for the Times released on Thursday suggested Sir Keir Starmer’s party held a 33-point lead over the Tories, with 54 per cent of the 1,712 respondents backing Labour.
Mr Jack said: “On opinion polls, I always give the same answer, which is the opinion poll that matters is when people go to the polls and cast their vote.
“We’ve seen opinion polls sway backwards and forwards, and while I’ve been in this role I’ve seen them move around dramatically.”
As an example, he pointed to a poll in 2019 that put support for Scottish independence among decided voters at 58 per cent before more recent surveys indicated support for the Union leading.
“Opinion polls are a snapshot of the mood of the country at the time,” Mr Jack said. “I prefer to look at the longer trends, but the one that really matters is when people go to the ballot box and that is two years away.”
When asked if Ms Truss and Chancellor Kwasi Kwarteng would continue on course, Mr Jack said there would be “more steps taken”.