Mrs Badenoch said taking charge of No11 was a “very, very low glass ceiling”, indicating that her party has now had four female leaders.
The mother-of-three joins Margaret Thatcher, Theresa May and Liz Truss as leaders of the Conservatives.
Her swipe came as she played down her own piece of history, after becoming the first black leader of a major UK political party.
Asked whether she was pleased people were noting the achievement, Mrs Badenoch told the BBC: “I think that the best thing will be when we get to a point where the colour of your skin is no more remarkable than the colour of your eyes or the colour of your hair.
“We live in a multi-racial country. That’s great but we have to make sure it doesn’t become something divisive.”
She added: “What I don’t want is for that to be the thing that ends up being talked about.”
Turning her fire on the Chancellor, Mrs Badenoch said: “I find it astonishing that Rachel Reeves keeps talking about how she’s the first female chancellor which in my view is a very very low glass ceiling in the Labour Party that she may have smashed – nowhere near as significant as what other women in this country have achieved.
Mrs Badenoch was declared the winner of the long-running battle to succeed Rishi Sunak on Saturday, seeing off a challenge from former immigration minister Robert Jenrick.
She is expected to unveil her shadow cabinet in the next 48 hours as she seeks to take the fight to Keir Starmer and the Labour party.
Loyal supporters, including Andrew Griffith, Claire Coutinho, Alex Burghart and Julia Lopez are expected to be rewarded with top jobs.
During the election campaign, Mrs Badenoch said she would offer jobs to her rivals although one, James Cleverly, has already said he will return to the back benches.
She has already offered Lord Houchen of High Leven, the Tees Valley mayor who did not back either candidate, the deputy leadership.
In her speech at the announcement she said it was time to “tell the truth” about where things had gone wrong for the Tories.
Pressed on the BBC’s Sunday With Laura Kuenssberg programme what had gone wrong with Boris Johnson’s government, Mrs Badenoch said: “I thought he was a great prime minister, but there were some serious issues that were not being resolved and I think that during that tenure the public thought that we were not speaking for them or looking out for them, we were in it for ourselves.
“Some of those things I think were perception issues, a lot of the stuff that happened around partygate was not why I resigned.
“I thought that it was overblown. We should not have created fixed penalty notices, for example. That was us not going with our principles.”
Stressing that the public was “not wrong to be upset about partygate”, she said: “The problem was that we should not have criminalised every day activities the way that we did.
“People going out for walks, all of them having fixed penalty notices, that was what ended up creating a trap for Boris Johnson.”
Mrs Badenoch said Britain needs fundamental change to stop getting “poorer”.
“I think that there are hard truths not just for my party, but for the whole country,” she said.
