Speaking to BBC Breakfast, she said the government would try to help people "perhaps secure those extra hours".
But a charity warned claimants would need to work up to nine extra hours a week to make up the shortfall.
Labour called the minister's remarks "an insult to hard working families".
Shadow work and pensions secretary Jonathan Reynolds later pushed his counterpart on her claims in the Commons, saying she had been "completely wrong" over the number of hours needed.
But while Ms Coffey said every UC payment "depends on the individual", she insisted there were "a number of different ways that people can actually earn more, keep more of their money, when they are working more hours" and on benefits.
Asked about her earlier comments, a Downing Street spokesman said the government was "supporting people to increase their incomes in a number of ways".
There are 5.9 million people receiving UC payments across the country, according to the latest government figures - almost double the three million making claims before the pandemic.
While some are seeking jobs and others are unable to work, 40% of claimants are already employed.
The £20 weekly rise in universal credit benefit was brought in during the coronavirus pandemic to help struggling families.
The government has said the uplift will be removed by October as it was always intended to be a "temporary measure".
But it has faced increasing calls from charities, opposition parties and even some Tory MPs, who think the cut would cause more pain to lower income families.
Asked about the reduction on Monday, Ms Coffey told BBC Breakfast: "I'm conscious that £20 a week is about two hours' extra work every week.
"We will be seeing what we can do to help people perhaps secure those extra hours, but ideally also to make sure they're also in a place to get better paid jobs as well."
But the Resolution Foundation disputed her figures, as claimants who work additional hours see their benefits reduced - or for each £1 they earn, the UC payment falls by 63p.
The charity said a UC claimant earning the National Living Wage - £8.91 an hour - and with an income of at least £6,100 a year, would take home just £6.60 for two hours work due to the taper in the payment, falling to £4.48 if they pay tax and National Insurance.
And they said the actual take home pay would fall to £2.24 an hour once any pension contributions or additional childcare or travel costs were taken into account.
This would mean they would need to work nine extra hours a week to make up for the removal of the £20 uplift.
Principal economist at the Resolution Foundation, Adam Corlett, said: "The government has tried to justify the coming cut to universal credit - and the huge income loss facing millions of households - by saying that it can easily be offset by simply working a few more hours. If only it were that simple.
"Many of those receiving universal credit aren't expected to work at all. And even for those in a position to work, a claimant on the National Living Wage will take a home as little as £2.24 from an extra hour's work.
"A small increase in working hours will be nowhere near enough to cover the £20 a week cut coming their way in just one month's time."
How much would your hourly wage have to be for two hours of extra work to make up for the lost £20 in universal credit?
Consider somebody who is entitled to UC and is earning enough to be paying income tax and National Insurance.
We estimate that they would have to be earning about £40 an hour for the numbers to add up, so £80 in total. Of that, £16 would go on income tax and £9.60 on National Insurance.
Universal Credit claimants have an amount that they are allowed to earn before their benefits start to be withdrawn.
Our example would lose 63p for every extra pound earned, knocking off another £34.27 of the £80, leaving them with £20.13.
Of course, somebody earning £40 an hour would be pretty unlikely to be on UC in the first place.
Labour also criticised Ms Coffey's remarks, with the party's deputy leader, Angela Rayner, saying the minister "either knows she's lying or shouldn't be in the job".
Mr Reynolds said the party would force a vote in the Commons this week "to give every MP the chance to back struggling families and cancel this cut".
Scotland's First Minister Nicola Sturgeon also issued a direct plea to Boris Johnson not to end the uplift - with the decision taken in Westminster for the whole of the UK, rather than being devolved.
In her speech at the SNP party conference, she said it would "quite literally take food out of children's mouths", adding: "If this deeply cruel cut does happen, the only conclusion it will be possible to reach is that Boris Johnson simply has no shame.
"Please, prime minister, for the sake of millions of desperate people across the country, do not let that be history's verdict upon you."
Asked about Ms Coffey's comments, No 10 stood by the end of the uplift. But a Downing Street spokesman said the government was doing numerous things to help claimants earn more.
"We are helping people learn new skills so they can progress to better jobs, indeed our Plan for Jobs provides a number of schemes which will help people learn these new skills and progress in their careers, and we are hiring 13,500 new work coaches to that end," he said.
"It is true we want to provide people with more skills and more training so that they can progress either in their chosen career or find another one."
There is a host of free guidance and advice available, including:
* The Money Navigator tool from the Money and Pensions Service relates to coronavirus-related money matters
* The Turn2Us charity has a benefits calculator
* Guidance is available from Citizens Advice and from the Low Incomes Tax Reform Group