Her opponent Rishi Sunak said he would seek to help pensioners and the most vulnerable with rising fuel bills.
Consultancy Cornwall Insight forecast that average bills could hit about £3,582 ($4,326) in October, up from £1,971 today, before topping £4,200 in the new year.
The two contenders vying to be the next prime minister have faced growing calls to detail how they would help with the energy price surge.
“We are facing great difficulties with energy," Ms Truss said.
"I understand people are struggling with their bills on fuel and food but the first thing we should do as Conservatives is help people have more of their own money.
“What I don’t support is taking money off people in tax and then giving it back to them in handouts. That to me is Gordon Brown economics.
“Frankly we had years of that under Labour and what we got was a slow-growth economy, and we didn’t get the opportunities, we didn’t get the enterprise, we didn’t get the new jobs in places like Darlington, which is one of the reasons people voted Conservative.
“What I fundamentally don’t agree with is putting up taxes and then also giving out benefits. I think that is the wrong approach."
UK Conservatives on the leadership campaign trail — in pictures
Ms Truss, the Foreign Secretary, also attacked the media several times during the hustings debate, before apologising to the journalist who hosted the debate as it concluded.
She accused “some of the media” of trying to “talk our country down” during the event, and of framing questions in a “left-wing way”.
But at the end of the debate she was caught on a microphone apologising to TalkTV journalist Tom Newton Dunn, who chaired the event.
The broadcaster was asking the South West Norfolk MP about her plans to help people with rising energy bills using tax cuts, when he mentioned “your handouts” as he sought to pose a question.
Ms Truss interrupted, saying: “They are not giveaways Tom. This is people’s money, but this is the problem with the way that every question is framed.”
“You’re framing it in a left-wing way Tom. I’m afraid the whole media does this all the time … it drives me mad."
Everything you need to know about Liz Truss - video
Ms Truss was later asked if Boris Johnson’s downfall as prime minister was of his own making, or someone else’s.
Some audience members shouted out, saying it was the “media”.
“Sounds like you’re being blamed Tom and, you know, who am I to disagree with this excellent audience?” Ms Truss said.
She said she was a “loyal Cabinet minister”, but did not directly answer the question, saying “what is done is done and we are where we are”.
“I believe in Britain, unlike some of the media who choose to talk our country down,” Ms Truss said later when talking about spending commitments and her plans.
“For the record, that’s the third time you’ve attacked the media – a lot of which supports your campaign,” Newton Dunn said.
As she hugged the host of the hustings at the end of the event, Ms Truss could be heard to say: “I am sorry I was mean about the media, Tom.”
Newton Dunn could be heard to reply that the jibes about the media were “cheap”.
Everything you need to know about Rishi Sunak - video
Mr Sunak, meanwhile, suggested he would not offer further cash payments to every household and would instead aim support at the most vulnerable.
Referring to earlier support that he approved as chancellor, he said: “I want to go further than I did previously because the situation is worse.
"It’s right that we target that on the people who most need our help.
“The only way to help them is with direct support because tax cuts alone are not much good if you’re a pensioner who is not earning any extra money.
“They are not much good if you are working hard on the national living wage, because Liz’s tax cut is worth about a quid a week for that person, it’s worth zero for a pensioner. That’s not right.”
Asked if he was planning support similar to earlier plans of providing £400 to every household regardless of their income, the former chancellor said: “No, because I think what we need to do is target our support for the most vulnerable.”
Mr Sunak said he would be happy to get in a room with Ms Truss and Mr Johnson to talk about future cost-of-living support before the result of the leadership ballot.
Asked earlier in the hustings the same question about whether Mr Johnson’s downfall was his own fault or someone else’s, Mr Sunak replied: “His own.”
Mr Sunak’s resignation as chancellor in July was regarded as a significant move to encourage Mr Johnson to leave his office.
He said the cross-party group of MPs due to investigate whether Mr Johnson lied to Parliament over partygate “will make the right decision” and he would “fully support” them.