The National Parent Forum of Scotland said a two-tier education system was developing, with some pupils able to take advantage of new technology and others hampered by slow internet speeds or poor equipment. The issue can be worse in rural areas which suffer from infrastructure problems, but a lack of investment by councils has also been blamed.
The criticism came after figures obtained through freedom of information legislation by Holyrood magazine found just 9% of Scottish schools could access internet at speeds of 100 megabits per second (mbps) or higher.
In January, the report of the ICT in Education Excellence group, commissioned by the Scottish Government, recommended that all schools should have a minimum bandwidth of 100mbps.
Iain Ellis, chair of the National Parent Forum of Scotland, said: "We are aware many local authorities are making progress on broadband width, but we do not think progress is being made quickly enough or consistently enough.
"IT infrastructure investment in schools is essential. Schools are often the only place now where children cannot access the internet and we believe they should be leading the way in internet learning.
"We are fearful of a two-tier education system - those with good internet access and those without it. It needs to be a priority."
A spokesman for the Educational Institute of Scotland (EIS) teaching union said ensuring all schools had access to high-quality, modern IT facilities should be a priority.
He said: "As more and more resources move online, including many of the resources that support the new curriculum and the new National qualifications, it is essential that teachers and pupils have ready and reliable access to the IT facilities to allow these resources to be utilised."
Education Scotland, which manages the network that provides connectivity to schools, said it was the responsibility of local authorities to provide the infrastructure that connects individual schools.
A spokesman said: "Work is being undertaken to consider the impact of infrastructure issues on schools and local authorities in the use of technology for learning and teaching including, wireless connections, bandwidth and bring-your-own devices."