Children were reportedly injured and left in tears as rocks and coins were pelted during violent clashes between Sheffield United and Middlesbrough fans.
More than 200 supporters were involved in trouble following their Championship game at the Riverside Stadium yesterday evening.
The shameful scenes saw children as young as 10 caught up in the violence and a police officer was injured amid claims that rocks and coins had been thrown.
Many fans took to social media to vent their frustration at the hoolligans responsible.
A Boro fan tweeted: "My friend got hit with a rock and I just dodged a coin. It was disgusting.
"We ran onto the bus before they broke through.
"There are kids on the buses who are crying. Disgrace!"
Meanwhile, many other fans have condemned the violence - and called for those who caused it to be banned from attending football matches.
Gary Schofield described those involved as a "minority who always ruin it for others and give the majority of fans and the clubs a bad reputation."
He added: "Hopefully they were caught on CCTV so that they can be punished and banned from football. Disgraceful to have children witness this."
Harry Chown added: "Even if it was a wrong decision - very ambiguous in a fast flowing game where the referee has no access to video footage - why would you brawl and fight?"
Mark Lowe said: "Sadly this spoils it for the family-type fans who like to support their club.
"Win, loose or draw you support your team by going to watch them not by scrapping outside the ground."
Gaye Noble-Wootton added: "There's always the elements out to cause trouble. They aren't true fans. Find them and ban them."
Cleveland Police said the violence began after United fans invaded the pitch to celebrate a late goal, which was disallowed, and then the clashes continued outside the ground in the car park.
Police and stewards attempted to keep order, however fans as young as 10 were caught up in the incidents.
A police officer also had to be taken to hospital with injuries sustained during the clashes.
Five people have been arrested on suspicion of a number of offences and are in police custody.
But the force warned that the number of arrests is expected to rise as the investigation unfolds.
Jason Harwin, a former South Yorkshire Police officer and current assistant chief constable of Cleveland Police, said: 'We will absolutely not tolerate violence of this nature and we will work to identify the offenders and bring them to justice.
"The vast majority of fans accept that football is a family game, watched by children, parents and grandparents. It's terrifying for children to witness such violence, or be innocently embroiled in it as their parents frantically try to keep them safe.
"Unfortunately a small minority of people behave in a manner which puts innocent fans at risk. We will be working closely with Middlesbrough and Sheffield United as part of our investigations."
Middlesbrough won the game 1-0 after Rudy Gestede's first half header.
Anyone with information that may help police are asked to call Cleveland Police on the non-emergency number 101.
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