Gary Neville has called for players to undergo diversity inclusion training when they move to the Premier League.
Cavani deleted the post and apologised, stating it was intended as an affectionate greeting to a friend.
Yet Neville argued that players should undergo inclusion training in order to educate them on diversity and discrimination.
“We hear the words education and training and yet football is still incapable of putting a curriculum in place for its players, for its members, for its fans that is compulsory,” Neville told Sky Sports.
“Why is Edinson Cavani not subjected to diversity inclusion training and education the minute he comes into this country?
“If we truly are going to root out discrimination in this country it has to become part of the curriculum, in school and within sport.
“Every employer in the country has to enter into a diversity inclusion training programme and implement it and execute it.
“Still to this day, in football, we have banners being held, players taking the knee, wave flags in the air and wear badges on our chest, where is the education and training? This could have been prevented.
“We are still going to continue to see incidents like this where Cavani reposted that Instagram story didn’t have a clue that he was doing anything wrong. And within 24 hours he is having to apologise for it.”
Neville says a host of organisations are to blame for players not being educated on diversity.
He said: “The Premier League, the FA, the EFL, the LMA and the PFA. They are all funded, they all have lots of money, put a diversity inclusion set of protocols and processes in place that are fixed that all five buy up to.
“We have five different slogans and they cannot even come together on a singular campaign on something they should be one on. At least collaborate on important issues that are societal. Drive it out of the game, root out discrimination and it has to be done by education and training.
“That means players and everyone that takes part in this game, including us, to bi-weekly or monthly training on diversity inclusion and why people take offence to certain words and why some people don’t.
“If it offends someone it is a problem.”
On the pitch, Neville hailed Cavani’s forward play after he inspired a comeback off the bench against Southampton.
“Ole Gunnar Solskjaer would have said at half-time ‘get one goal’ and the first was the big goal in the match for United,” Neville said. “At that point, you’re then thinking Southampton will have to score again as it was a different game.
“For the second, Cavani is one of the best and has been for years – we played against him with England – at making that run in and around the near post.
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Manchester United secured a dramatic comeback victory at Southampton on Sunday, largely thanks to Edinson Cavani’s two goals off the bench.
Bruno Fernandes’ goal set Ole Gunnar Solskjaer’s side on course to battle back from 2-0 down at St Mary’s, giving United a third successive Premier League win.
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“He does it all the time, he’s always there making that movement across defenders. The ball came out to the edge of the box and, as it came to Fernandes, Manchester United have got four players in the box but the one that’s on the move, the one with the instinct, is the goalscorer.
“I’m not alerting something to the other clubs that they don’t already know – his first touch in English football, he went across the near post, which he will do every single time.
“You know it’s coming but whether you can stop it is still a problem.”