The demonstration, which was organised by Equalities and Human Rights UK and Sparkle Sheffield, saw 250 people march from Devonshire Green to the Town Hall for a rally on Saturday afternoon. Campaigners say the authority is using finances rather than needs to shape its policies for youngsters with autism and other learning disabilities.
They say children are missing out on places at special schools because the council is taking too long to set up education, health and care plans.
The plans are legally binding agreements that cost councils money.
Director of Equalities and Human Rights UK, Chrissy Meleady, said she was pleased with the turn-out at the demonstration, and said this was just the beginning of the campaign.
She said: “We have told the city council that we are prepared to hold sit-ins, more demonstrations, whatever it takes to get the best education and care for our children.”
Chrissy added: “The council apologised for delays in administration but not for anything else - not for the failings that have seen some children being out of school for as long as 16 months.
“These decisions have a big impact. Some of these children who aren’t in the right school, have been pulling out their hair, pulling out their eyelashes, pulling out chunks of their arms because they’re not in the right place for them.
The council admits it has made mistakes, which the authority this week said it ‘truly’ regretted.
Mum Kerry Arliss attended the demonstration with her seven-year-old son Harry Hayes, who has severe autism.
Kerry, of Grenoside, says Harry was given a place at the Robert Ogden school, which specialises in education for children with autism, but was forced to give up the place when the local authority said they could not fund his education there.
The 28-year-old said: “He’s a lovely boy, and given the right provision he would be able to live the life he deserves.
“But he’s not in the right school for him, so he gets frustrated and kicks off.
"He’s at Grenoside Primary School - and they’re all amazing there.
“They do everything they can to help him - but mainstream education is not the right place for the needs he has.
“He ends up just walking around for hours to get away from the other children because he’s causing them harm.”
Dozens of children also attended the demonstration dressed in superhero costumes.