The Belgium international was dismissed by referee Chris Foy after he lost patience in last night's Capital One Cup semi-final second leg match in south Wales as ball boy Charlie Morgan refused to hand over the ball after it had gone out of play for a goal-kick.
The incident happened near the end of the match with the sides tied at 0-0 – and Chelsea trying to make up a 2-0 leeway from the first leg.
Morgan fell to the ground as Hazard tried to get the ball from him, with the Blues forward then trying to kick it from under him but appearing to instead make contact with the youngster.
Asked how he would have reacted to the situation, former Scotland international Nevin said: "I would have kicked the ball out from underneath the ball boy if he had been lying like that."
Nevin also criticised the behaviour of 17-year-old Morgan, branding it "disgraceful".
He added: "I was very, very disappointed by the way the ball boy acted, and I say 'acted'.
"He must have been watching footballers, the way he rolled around and pretended to be more injured. He only has one job and his job is to go and give the ball back, and what did he do? He keeps the ball. His behaviour was disgraceful."
There has been criticism of Foy for his dismissal of Hazard, but former Premier League official Dermot Gallagher praised his handling of a difficult situation – as the FA today said they would review footage of the incident.
He said: "The referee has taken the correct action.
"It's against the laws of the game to commit violent conduct on anyone under the jurisdiction of the game."
Swansea vice-chairman Leigh Dineen, meanwhile, placed the blame squarely at the door of the Chelsea man.
"You can't kick out at anybody. If it was done on the field of play, there would be questions to be answered," he said.
The incident overshadowed Swansea's achievement of reaching their first major cup final in their centenary season, just 10 years after being bottom of the Football League.
But Dineen was able to see the lighter side of events at the Liberty Stadium, joking that Swansea may consider taking their own ball boys to the Wembley final.
"If we need to," he said. I am sure Wembley will have their own."