The group In-Care Abuse Survivors Scotland (Incas) wants the inquiry to look at cases including the notorious Magic Circle scandal involving a leading QC and former Tory MP Nicholas Fairbairn.
But the Scottish Government has refused to extend the scope of the inquiry beyond abuse which was suffered by those in residential care.
In a letter to the inquiry team, Alan Draper, Incas’ parliamentary liaison officer, said victims abused outside residential settings felt excluded.
He said: “The submission made by Incas to government was that the inquiry should cover all organisations and institutions who had a duty of care for young people.
“The government, however, limited the remit primarily to residential institutions. This has resulted in many victims who suffered grievous abuse being excluded.
“It has also enabled institutions and organisations who have covered up criminal activity to escape public scrutiny and possible prosecution. The government, by its failure, has effectively become complicit in that cover-up.”
Last year, Susie Henderson, the daughter of the late QC Robert Henderson, said she was abused by her father and former Tory MP Nicholas Fairbairn - a former solicitor general for Scotland who died in 1995 - from the age of four.
She claimed the men were members of an organised paedophile ring which abused her in her family’s house in Edinburgh and other locations.
Earlier this week, another survivors’ group, White Flowers Alba, threatened to take legal action in a bid to force the remit of the inquiry to be extended.
A Scottish Government spokeswoman said: “There are a wide range of survivors with differing views but many have told us that they did not want a scope that was so wide that it would never report in a reasonable timescale.
“For the inquiry to succeed and reach clear conclusions and recommendations it must focus on an set remit and timeframe.
“All allegations of criminality will be a matter for the police.”