One of them disrupted a penalty by kicking the ball away and barging into Harry Pell, who subsequently missed the spot-kick.
The shameful scenes followed more unsavoury behaviour at away games at Fleetwood and Crewe, where the linesman was hit with an object.
And Stewart says the club will not tolerate “hooliganism”.
“We're proud of the fans at Rotherham," he said. "We're gathering more and more supporters. Families are coming.
"I'm sure the fans want what we want. They don't want hooligans, they don't want us to get a bad name because one or two idiots are spoiling it for the many.
"The fans here have been fantastic. They've supported me for the last 14 years. We want a good name, not a bad name.
"Rotherham are better than that. Anyone seeing someone acting untoward needs to report it to the stewards and we'll take the necessary steps from there to make sure we stamp it out."
The Millers could be handed a hefty financial sanction by the governing body if they are found guilty of a charge.
Stewart says that could do reputational damage to the club.
“At the end of the day, I like us to manage our club in the way that it needs to be managed. “We don't want governing bodies coming in and giving out fines that have to be paid by the club.
“All it does is erode the good name we've built up over many years.
“Rotherham have a good standing and if we're not careful we're going to bite into that. That wouldn't be good for the club or the town and wouldn't be fair on all those fans who come and support us week in, week out.
“We're all together. I have to make sure we get rid of these bad elements that have sprung up in the last few weeks. We won't tolerate it and I will take any action that's appropriate.”