Di Canio, who had pleaded guilty to a charge of misconduct, said after the hearing: "I am very, very sorry for what happened. I had a fair hearing, for which I am grateful."
His club, who had themselves suspended Di Canio after the incident, said they would not appeal. "We are satisfied with the outcome," Howard Culley, a Wednesday director, said.
"We fully accept the decision. There will be no appeal. During the hearing Paolo apologised. He apologises to the commission, he apologises to the referee, he apologises to the club and its fans."
The ban will keep Di Canio out of action until, ironically, Boxing Day, when he will be eligible to play for the Owls when they meet Leicester at Hillsborough. Both Di Canio and his club said yesterday they were looking forward to the player's return, and there was no suggestion he will abandon the English game as had been thought was a possibility.
The match against Arsenal was marred by a brawl involving several players just before half-time. The Italian was shown the red card by Alcock and reacted by shoving the official in the chest. Alcock stumbled backwards and fell awkwardly to the ground. Alcock, who has said he will continue to referee matches, was not at yesterday's hearing as Di Canio had already admitted the charge.
David Davies, the FA's director of public affairs, said: "Paolo Di Canio apologised for what had happened. He apologised to the FA, to the referee, to his club Sheffield Wednesday and its supporters. He said he had made a big and a bad mistake. He lost his head for two or three seconds and it will never happen again.
"The commission was told by Sheffield Wednesday that the case was unusual because Mr Alcock had fallen to the ground. The media suggestion Paolo Di Canio had claimed the referee had fallen deliberately was vehemently denied on his behalf. It was also said that he had acted out of character. He had never intended to harm the referee. He had brought shame on himself.
"The commission viewed various videos in connection with the case. They decided Paolo Di Canio should be banned from football for eight games on top of the three he will automatically miss for his sending off.
"This punishment includes the one game he has missed already on the orders of his club. He has been fined pounds 10,000. In line with natural justice the commission said they hadn't come to their conclusion purely so the penalty should act as a deterrent. They considered what happened considerably more serious than normal on-field offences.
"Following today's hearing the commission was unanimous that an urgent recommendation should go to the FA's disciplinary committee to ask that it should be made clear to all concerned that stronger penalties should be imposed immediately on any player who manhandles a match official."
Di Canio's shove on Alcock was not the first time he has been in trouble in England. After joining Wednesday for a club record pounds 4.5m last year he was soon in trouble with the FA for mooning on the pitch in celebration of a goal, and then in January he was sent off in an FA Cup replay for swearing at the referee. Yesterday's ban was criticised as being too lenient by Philip Don, who represents Premier League referees. "It is fair to say I am disappointed with the verdict because I thought it would be longer," he said. "Paolo Di Canio has been found guilty of a major disciplinary issue and I don't think the punishment is correct."
Gordon Taylor, the Professional Footballers' Association chief executive, said: "At the top level the game, and the way it is carried out, is looked at by the people who play it in the parks and really we've got to set good standards."
Some might argue Di Canio got off lightly. As recently as 1954, Willie Woodburn, a Rangers' player, received a life ban after collecting five red cards, and more recently still, Eric Cantona was banned in for eight months in 1995 and fined pounds 10,000 for karate kicking a fan who had abused him.
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