The Location, Location, Location presenter was widely criticised for comments she made in the Sunday Times that she bought her first home at the age of 21, with the help of her family, by saving on luxuries.
Allsopp tweeted: "The Sunday Times have reviewed the tape of my interview with them and agreed that I never said I was enraged by people saying they could not afford to buy a home.
"The unaffordable nature of homes in many parts of the UK is something that has concerned me for a long time. The impact of this on society as a whole is very serious.
"The premise that I had no sympathy or empathy for those who can’t afford to buy a home was entirely false. It struck at the heart of the work I’ve done for over 22 years, and in our internet age nothing is tomorrow’s chip paper."
The Times printed in the Letter to the Editor column: "In an interview and subsequent news story we reported Kirstie Allsopp as saying, 'I get enraged when people say they can't afford to buy.'
"We are happy to accept that Ms Allsopp in fact said, 'I get enraged when people say that young people can't buy,' and that she has spent much of her career helping young people find homes they can afford to buy."
Property expert and craft-lover Allsopp, 50, is now questioning the size of the apology.
She said: "Obviously this won’t repair the damage done or get back the two weeks lost to fending off the abuse, and forcing the Sunday Times to admit they’d made up things to create controversy and clicks. Nor can I do much about the other papers or the stuff on TV or Radio, not to mention the abuse on social media."
She added: "I still believe that if you find the right person to talk to about today’s housing issues, which are going to create such problems for the future if we don’t address them, it might be possible to change things."
Allsopp had been quoted as saying: "When I bought my first property, going abroad, the EasyJet, coffee, gym, Netflix lifestyle didn't exist.
"I used to walk to work with a sandwich. And on payday I'd go for a pizza, and to a movie, and buy a lipstick.
"Interest rates were 15 per cent, I was earning £11,500 a year."
She added: "I don't want to belittle those people who can't do it. But there are loads of people who can do it and don't...
"It's about where you can buy, not if you can buy. There is an issue around the desire to make those sacrifices."
Allsopp has presented Channel 4 property show Location, Location, Location with Phil Spencer since 2004.
She also hosts crafting shows on the channel including Kirstie's Homemade Home.
Piers Morgan called the TV presenter "unbelievably stupid and privileged" for her comments.
It is not the first time former Good Morning Britain presenter Morgan, 56, and Allsopp have clashed on Twitter.
Last year, he called her "cretinous" for saying that lockdown was more dangerous to children than COVID-19.
The Keep Crafting And Carry On presenter tweeted: “COVID is a horrible disease but it is very, very, very rare for it to impact children. They are still at far more danger from journeys in cars, or swimming, or trampolining than COVID. Please do not let anyone persuade you otherwise.”
Morgan responded: “Of all the people I least want to hear from when it comes to expert advice on coronavirus, TV estate agent Kirstie Allsopp and her cretinous trampoline analogies are top of the list.”
Watch: UK property prices continue to rise