Eddie Howe says they could cause a tragedy, as pitch invasions and fan violence have marred English football in recent days.
There have been five pitch invasions, players being attacked, Crystal Palace boss clashing with a fan and investigations launched.
It is an offence for fans to enter the pitch without lawful authority or lawful excuse, according to the Football Offences Act 1991.
What is happening and what will happen next?
Harry McKirdy said he would take the stick and the songs. But bottles, coins, lighters thrown at me, running on and hitting and kicking me/team-mates. Too far.
His manager said that it was absolutely disgusting, but he didn't know where we were going as a country.
He believes that celebrations can take place without pitch invasions if his side wins the title on Sunday.
It could have been dangerous. He said he was not sure how to avoid that.
I don't want to judge. For the other team it is dangerous. I hope we learn from that. Absolutely nothing should happen.
We can celebrate things without threatening ourselves or the opponent.
Howe, who takes his side to the bottom of the table on Sunday, said: "I don't mind the celebrational aspect - embracing the success that a team has had is part of football."
There is a lot of people around one or two people.
We have to act very quickly because we want to avert potential tragedy.
Dean Smith said more needs to be done to protect players.
I don't think we are doing enough about security, he said.
Football fans, we missed them during the Covid period, but come on, you don't want to be attacking people and managers.
In general society, you can't go and abuse anyone on the street, but for some reason you're allowed to do that at football. It is a big concern at the moment.
Fans have been present in stadiums since the start of the Covid-19 epidemic in March 2020.
The professor of law at the University of Manchester, who studies crowd behavior, said that the effects of the lockdowns have caused a decline in the behavior of some fans.
There is a certain element of fan desire to be seen as authentic after the first major pitch invasion.
What is authentic fan behavior?
Unfortunately, at the moment, running on to the pitch, setting off smoke bombs, is what authentic fans are doing.
Mark Roberts, the national lead for football policing, said in February that cocaine use is helping to drive a rise in disorder at matches.
Anyone caught in possession of or supplying class A drugs in connection with football will face a five-year ban and their passport will be taken off them.
Police data shows that arrests at football matches in the top five English Leagues are at their highest levels in years.
The Professional Footballers Association called for a review of matchday security and fan disorder after the Sharp incident.
He said the violence seen this week in football is disgusting andbizarre.
Billy Sharp got stiches in his face because he had to take the nut from an idiot, so it will be stopped for next season. He said that it cannot happen again.
Billy Sharp banged his head and never woke up.
Andy Holt, chairman of Stanley, said on social media that it is a disaster. Stay away if you cannot cope with that.
You are ruining the day for many, increasing club security cost and as a result ticket prices for all. I am not paying extra costs because of these stumps.
If costs go up, tickets go up. We don't need them in football so we should ban them all and jail them all.
Frank Lampard doesn't see pitch invasions as an issue if fans behave.
If it is done in the right way, let them stay on the pitch, as long as they behave.
The rise in the number of pitch invasions was alarming and Chief Constable Roberts called on fans to celebrate in the correct way.
The pitch is the players place of work and they should be able to feel safe.
The consequences of such behavior can be severe, as was discovered by the fan who headbutted Sharp. He was fined and given a 10-year football banning order.
A suspended prison sentence was given to a fan who threw a plastic bottle at a group of players.
Pearson believes a lot of legal action will have to be taken against a lot of people in the close season as fans who have been involved in violence during the pitch invasions are identified.
Football banning orders prevent people from attending games for three years, and they can be asked to give up their passport to prevent them from going to games. Those who violate the orders will be sentenced to six months in prison.
The Crown Prosecution Service is giving advice on how to build the strongest cases against fans who attack players.
On Wednesday, the EFL said it was to consider what further measures were at its disposal in order to tackle crowd behavior.
The FA has the power to order ground closings for issues involving supporters, while clubs have previously been fined.
The two most significant fines in recent times were West Ham being fined 100,000 for fans going on to the pitch during a game against Burnley in London Stadium in 2018, and Villa being fined 200,000 for their fans going on to the pitch multiple times in 2015.
A fan went on to the pitch and punched Jack Grealish during a derby game in March.