Football should strive to be at a point where stewards are no longer required to control crowds, according to Gareth Southgate.
The England manager said that fans should have the capability of behaving themselves at matches without the assistance of security.
Southgate, 48, insisted that football had become a "much friendlier place" since his playing days in the late 80s and 90s, but maintained more needed to be done to ensure a "secure" environment for players and spectators alike.
Describing how the weekend's incidents had not shocked him, Southgate said: "If you go down many high streets at the weekend, unless you're oblivious to what goes on in our country, there are, unfortunately, scenes of inappropriate and anti-social behaviour.
"So to see that inside of a football ground is disappointing for us as a sport, but it's a societal problem as much as it's a football problem.
"I think everybody would want to work together to make sure the right security measures are in place, but, frankly, we should be living in an era where we don't need stewards.
"Why should we need stewards to control a crowd? We should be able to go and watch a football match and behave ourselves.
"Clearly some people are unable to do that, so everybody's got to work together to make sure the environment is secure for players and other supporters as well."
Southgate said that he hoped punishments would be severe enough to deter anti-social behaviour.
Paul Mitchell, the Birmingham City fan who attacked Grealish, was jailed for 14 weeks on Monday over the incident.
"I think that some of the punishments that are handed out, hopefully, will act as a deterrent," Southgate said.
"But you have to appeal to people, that they recognise what is acceptable behaviour, in society, really.
"The game has become a much friendlier place over the 20-30 years I've been involved, for families to come to, for women to come to, for children to come to and we want that, we want it to be a place where everybody feels that they can bring their family and feel safe and enjoy themselves.
"So it would be a huge disappointment if we drifted back to the way the game was in the period when I was growing up."
Asked whether he thought the Nations League, like the World Cup, would bring a sense of unity to the country at a time of political turmoil, Southgate said he hoped the football would excite fans.
"I think, generally speaking, people from any country like to get together and celebrate national events," he said.
"We can't keep relying on the royal family to produce babies and have weddings, so there's got to be other methods of doing that.
"If we can provide hope and optimism through our performances, then that's part of our responsibility as a team.
"We always want to play in a way that excites people. We want a team that the public are proud to watch and we hope to play our part. Whether [or not] we can resolve all the issues in our country is a more difficult task."