As the government plans to provide an extra £20.5bn funding for the NHS by 2023 to 2024, pension tax relief has been viewed as one of the likely targets of cuts in the next Budget.
Ms Morgan said: "The Treasury has not moved on several of the committee's recommendations, or demonstrated an increased sense of urgency required in some key areas identified by the committee.
"We will continue to hold the government to account for its record on improving household finances."
According to Tom Selby, senior analyst at AJ Bell, ripping the roots from the pension tax system just as automatic enrolment is bedding in would have been a monumental gamble by 'Spreadsheet Phil'.
He said: "Fundamental reform as some have suggested – such as introducing a flat-rate of tax relief – would hit right into Conservative heartlands and risk causing a rebellion among backbench MPs already riled by the Brexit negotiations.
“More importantly, it would risk the fragile savings culture being nurtured in the UK through automatic enrolment.
"Lack of saving remains arguably the biggest challenge facing society today, so anything that could potentially damage this needs to be avoided at all costs. The pragmatic approach being taken by the Government therefore feels like the right one at this time.
"The government is also right to knock back calls for the Lifetime Isa to be scrapped altogether. Criticisms of the new savings vehicle didn't appear to be based on any hard evidence.
"In fact, the Lifetime Isa has proven popular among younger savers and ditching it now – just as it gains traction in the UK – would have been a retrograde step."
Gem Durham, independent financial adviser at Obsidian, agrees that a single rate of tax relief would be fairer.
She said: "But I see a Labour government being more likely to bring that change in rather than a Conservative led one, and I would envisage it would be something that a government would want to do at the beginning of a term in office and not close to when there might be a general election – which is a possibility in the near future."
Regarding the Lifetime Isa, Ms Durham is pleased with the government's decision.
She said: "For basic rate tax payers, Lifetime Isas are more beneficial than pensions. I think this is a massive incentive to younger people who are in their 30’s or 40’s (you can continue to contribute until 50, as long as you started before 40).
"Ministers are so out of touch with the british public and their day to day worries and concerns. If they promoted Lifetime Isas properly and raised threshold to £10,000 (£8,000 with £2,000 bonus) per annum, they could solve a lot of the lower end of the middle classes savings problems.