Seven people have now been arrested, six for violent disorder and a seventh for possession of an offensive weapon, police said.
Twenty police officers were left injured, two seriously, following the riot on Sunday night.
It started as a peaceful demonstration but turned violent after about 500 protesters descended on the New Bridewell police station.
Speaking to broadcasters at BAE Systems in Preston, Mr Johnson said: "I think all that kind of thing is unacceptable and the people obviously have a right to protest in this country.
"But they should protest peacefully and legally."
Two of those injured were treated in hospital after suffering a punctured lung and broken ribs, and a fractured arm, respectively. Both have since been discharged.
Police said between 2,000 and 3,000 people had gathered at College Green on Sunday to protest against the Government's Police, Crime, Sentencing and Courts Bill, which will see the police handed new powers to tackle demonstrations.
Andy Marsh, chief constable of Avon and Somerset Police, said the demonstration had been "hijacked" by several hundred "extremists".
"I believe the events of yesterday were hijacked by extremists, people who were determined to commit criminal damage, to generate very negative sentiment about policing and to assault our brave officers," he said.
"From the initial gathering of around 2,000 to 3,000, which was more than we anticipated, there were about 50 officers engaging with those present and encouraging them to disperse.
"There was a hardcore of serious criminals hidden within those 3,000 people - perhaps 400 or 500 people - and we certainly didn't trigger this.
"The officers were incredibly patient, incredibly professional and I pay tribute to them."
Mr Marsh said 12 police vehicles were damaged, including two that were set on fire, and "significant damage" was caused to the New Bridewell police station.
"I'm incredibly saddened by the dreadful scenes we saw here," he said.
"Officers were pelted with stones and missiles and fireworks and it was a terrifying situation for them to deal with."
The chief constable said there had been no prior intelligence to suggest any disorder was planned on the scale seen.
"A tactical decision was made to deal with these criminals retrospectively and not make a significant number of arrests last night," he said.
"This would have impacted significantly on our resources at the scene and created a greater risk of damage to property and injuries to the reduced number of officers left to deal with the disorder."
Home Secretary Priti Patel said the scenes were "unacceptable", and "thuggery and disorder" would never be tolerated.
She told the Commons: "The scenes in Bristol yesterday were utterly shameful. We saw criminal thuggery and disorder caused by a minority who put lives at risk.
"Our exceptional and brave police officers put themselves in harm's way to protect the public. For them to face the criminal violence against them while upholding the law is completely unacceptable."