The comments came on the same day that his party suffered historic losses in the local elections in Leeds, with seats in both Guiseley and Horsforth turning Labour for the first time in their history.
It reflected a national picture, with Labour making gains, but the Conservatives losing hundreds of council seats across the country.
Speaking at the election count on Friday, Conservatives group leader Andrew Carter said: "Cost of living came up on the doorstep all the time.
"There is a perception that the government should do more to try and help the people who are feeling the pinch.
"The government has to think of new ways of trying to help. They helped people tremendously during Covid."
Chancellor Rishi Sunak was criticised during his Spring Statement earlier this year, as he gave no mention of any help for those on universal credit, despite the controversy around the Government's scrapping of the £20 uplift to those on the lowest incomes.
Among the announcements from Mr Sunak was a 5p cut in fuel duty to last until March 2023. He also decided the national insurance threshold would rise from £9.500 to £12.500 from this July.
Since then, the energy price cap has increased by more than 50 per cent, meaning many are paying hundreds of pounds more a year for gas and electricity.