The goal of levelling up is to provide equal opportunities across the UK.
A news Panorama investigation raises questions about whether money is reaching the most deprived areas in England.
Mr Gove said his department was helping councils to ensure bids are effective.
Levelling up was a key part of the Conservatives’ 2019 election campaign.
The government recently set out its 12 “missions” for the policy – ranging from improving education to faster broadband capability to local transport – with a deadline for delivery in 2030.
“Unless we stick to those missions, then the cost of living issues that we face at the moment will deepen inequality,” said Mr Gove.
Labour’s Lisa Nandy, the Shadow Levelling Up Secretary, said the government should begin by getting inflation under control. “By their own admission, their mismanagement of the economy is going to make levelling up harder,” she told Us.
For the first round of the so-called Levelling Up Fund, £1.7bn has been allocated to towns and cities across the UK.
When Panorama sent freedom-of-information requests to councils in the 100 most deprived areas in England, it found that 28 councils had all their bids rejected. This included 18 areas that were on the government’s top priority list, including Knowsley and Blackpool.
Meanwhile, 38 councils won all, or some, of the money they requested, and 34 councils did not submit a bid in this round.
A second round for the fund will open for applications at the end of May.
Former government economist Nicola Headlam said asking councils to bid against each other was not the right approach. “A beauty contest around who gets the money, that’s not really how I would do it,” she said. She also said that affluent places could have more resources to write better proposals.
Mr Gove said his department was deploying levelling up directors, who live in the relevant areas, to assist with bids.
Data methodology: Data gathered under Freedom of Information requests to lower tier local authorities. We have excluded any bids made at a county council or combined authority level as these had more limited eligibility criteria for the Levelling Up Fund. We used the Index of Multiple Deprivation 2019 ‘rank of average ran’ summary measure. Corby has been excluded due to boundary changes, so we included the 101st-ranked local authority Nuneaton and Bedworth.