Council leader Councillor Cecil Meiklejohn says the full impact of measures agreed with the Scottish Greens to get the budget over the line will first have to be studied in detail.
She said: “Following the recent amendment to the Scottish Government budget Falkirk Council will need to re-assess the impact of the changes and the implications, and revisit officer proposals, which members will then give consideration to and make a final decision at a meeting of the council on February 27.”
Mike Kirby, Scottish secretary of the union UNISON, said: “This deal does not maintain funding for even current levels of public services.
“We of course welcome any extra funding being proposed, however the local government settlement falls short of what UNISON and COSLA agree is necessary to maintain even current council services”.
Finance Secretary Derek Mackay’s plans for 2019-20 were passed by 67 votes to 58 on Thursday, with critical help from the Greens.
Among those dissatisfied with the budget is the Public and Commercial Services union, representing thousands of Scottish civil servants, which says longstanding pay concerns have not been addressed.
Spokeswoman Lynn Henderson said: “We are prepared to pursue this issue until our members get a decent wage that addresses the decline they have experienced for a decade.”
Teachers union the EIS says plans to give councils power to introduce a parking tax for businesses and other employers could translate into an extra cost passed straight to employees.
It adds that while the level of the fee would be up to the council one scheme operating in Nottingham charges £415 per space, while one West London council aims to bring in a levy of between £500 and £1,000.
The move has been welcomed by Friends of the Earth Scotland, which argues it will help to cut pollution and lend new importance to the need to create effective public transport.
But the union UNISON says it appears to undervalue the contribution to local life made by council and similar employees.
CBI Scotland is broadly supportive of the budget, commenting: “On business rates, the scrapping of the proposed out-of-town levy, capping the poundage rate and confirming the switch from RPI (retail price index) to CPI (consumer price index) for the duration of this parliament are all welcome and will support businesses to grow the economy.
“If there is an added winter chill in the air, it’s the growing income tax gap between Scotland and the rest of the UK, alongside the emergence of a new ‘tourist tax’”.
That particular innovation follows years of arguments, and has been bitterly opposed by the hospitality industry - but supported by Edinburgh Council.
Falkirk West MSP Michael Matheson, meanwhile, says the budget proposals will give a cash boost to vital public services in Falkirk district and offer economic stability in the face of Brexit uncertainty.”
The budget is proposing additional funding of almost £730million for Scotland’s health and care services, including a 4 per cent increase in funding for NHS Forth Valley from £506.8million in 2018-19 to £527million.
Other moves include the setting up of a £50million fund to support town centre initiatives.
A final vote on the Bill is due to take place on February 21.