After the government's fiscal policies unnerved the markets, Ms Truss said she had “adjusted what we’re doing” by tearing up her policies to “restore economic stability”.
“I do think it is the mark of an honest politician who does say, yes, I’ve made a mistake,” she told the BBC.
Ms Truss will meet her cabinet on Tuesday with ministers in every department to be told to find cuts.
After new Chancellor Jeremy Hunt scaled back the energy support package and ditched “almost all” of the tax cuts announced by his predecessor, Ms Truss said she wanted to “accept responsibility and say sorry for the mistakes that have been made”.
“I wanted to act … to help people with their energy bills to deal with the issue of high taxes, but we went too far and too fast. I’ve acknowledged that,” she told the BBC.
She said she was “sticking around” because she was “elected to deliver for this country”.
“I will lead the Conservatives into the next general election.”
The five candidates vying to replace Liz Truss - in pictures
Earlier on Monday, Mr Hunt said he believed Ms Truss would still be prime minister at Christmas.
In an interview with Sky News, the new Chancellor called on Conservative MPs to "give her a chance".
Mr Hunt ruled out becoming prime minister himself: "I rule it out, Mrs Hunt rules it out, three Hunt children rule it out."
"She's [Ms Truss] Prime Minister, she has got important decisions to make.
"People who want her to go need to ask themselves whether more political instability is going to help keep mortgage rates down, keep interest rates down, calm the markets.
"I don't think political instability is the answer. She's been Prime Minister for about five weeks and we need to give her a chance."
"I would rather a leader who listens, learns and changes and I think we would have more instability, much more instability, if we were to have a leadership process."
Liz Truss's political career - in pictures
The pressure on the prime minister gained traction on Monday evening with five Tories openly calling for her to go after just six weeks in power.
Sir Charles Walker was the latest to make the case for her exit.
“I think her position is untenable. She has put colleagues, the country, through a huge amount of unnecessary pain and upset and worry,” Mr Walker told Sky News.
The situation “can only be remedied” with “a new prime minister”, he said.
Earlier, the prime minister’s press secretary said at no point on Monday did Ms Truss think her time was up.
Conservative Party chairman Jake Berry said there had been a focus on “unity” as she addressed a gathering of the One Nation group of Tory MPs in Westminster.
Mr Berry said she had been “exceptional” and he had not heard any irritation towards her in the meeting, although it was still going on.