Public services face a “perfect storm of financial pressures”, the Welsh government said as it unveiled its spending plans for next year.
Finance Minister Rebecca Evans said her £20bn budget would top up NHS funding and help vulnerable people through the cost of living crisis.
But ministers have ruled out raising income tax, despite calls from Plaid Cymru to use it to bolster pay rises.
There are increases for health and councils.
But there is concern for homelessness support as a grant scheme faces a real terms cut.
Meanwhile, ministers confirmed that winter fuel payments worth £200 for people on benefits would not be offered from April.
It comes as the Welsh government faces pressure over pay from unions, with nurses set to strike on Thursday.
Labour has said a lack of funding from the UK government makes it unable to offer better pay deals but Mr Drakeford said in October that the case for tax rises would be considered.
The Conservatives said there were questions to answer over how effectively money was being spent by ministers.
More for health and councils – but services face cuts
The Welsh government sets funding for the health service and for councils, who in turn fund social care, schools and refuse collections.
But services could struggle to meet increasing costs – meaning they may face difficult choices and potential cuts.
In its announcement it said an extra £165m was allocated for NHS Wales to help protect frontline services.
Overall the health and social services spending will increase by 6.31% to £10.9bn – less than the consumer price index inflation rate of 11.1%.
It comes amid demands for pay rises to meet the cost of living, with members of the Royal College of Nursing (RCN) walking out on Thursday.
RCN Wales director Helen Whyley said: “The Welsh government have no intention of offering a resolution and the draft budget today only confirms that.”
An extra £227m was provided to councils – which includes cash for schools. Head teaching union NAHT Cymru warned it was not enough to solve the funding crisis in schools.
There is no extra money for Natural Resources Wales, which sees its budget stay at £60.1m, while ministers also said they are “unable” to help the heritage and culture organisations that it supports meet the pressures of inflation.