The YouGov research shows 44% of Scots think the SNP administration is performing well when it comes to education and schools, a drop of five points since August.
On health, 43% have a favourable view of how the NHS is being handled, also down five points, while justice has dropped four points to 42% and the economy is down one point to 41%.
The poll also revealed a drop in satisfaction in Scotland’s rail services amid criticism of ScotRail operator Abellio, Network Rail and Transport Minister Humza Yousaf over train performance.
The proportion satisfied with train services was 58%, down from 68%, while 31% were dissatisfied - up from 23%.
Mr Yousaf has said he wants to work with unions and other political parties to put together a public sector bid to run the railways.
A majority (58%) of Scots back the move, while 19% do not, with net support for the measure rising from 35 to 39.
YouGov polled 1,134 Scots between November 24 and 29.
A spokesman for First Minister Nicola Sturgeon said: “These findings show strong backing for the SNP in Government across a range of policy areas, after nine years in office.
“But over the coming months we will be working harder than ever for the people of Scotland, helping to build our economy and create jobs and continuing to deliver first-class public services.
“However, the threat to jobs, the economy and public services from a Tory hard Brexit is a very real one, which is why we are pursuing every avenue to maintain Scotland’s place in Europe and our continued membership of the single market.”
Scottish Labour business manager James Kelly MSP said: “This poll shows that Scots are losing confidence in the SNP’s ability to run our public services.
“A decade of SNP mismanagement of our NHS has created a workforce crisis with nine out of 10 nurses saying their workload has become worse and a third of NHS staff saying there aren’t enough of them to do their jobs properly.
“These problems did not appear overnight, they happened on Nicola Sturgeon’s watch when she was health secretary.
“The SNP claims that education is its top priority, but the gap between young people’s achievements in our most and least deprived areas is shocking. This is too important an issue for the Government to be distracted by dreams of independence.”