Ferguson appealed against the charge and requested a paper hearing.
However, the verdict, which has been released by the FA Friday afternoon, has gone against the Scot.
"Following an Independent Regulatory Commission hearing today, Sir Alex Ferguson has been fined £12,000 in relation to media comments made after Manchester United’s game at Tottenham Hotspur on 20 January 2013," said an FA statement.
"It was alleged that the Manchester United manager’s post-match media comments implied that the match official was motivated by bias.
"Ferguson had denied the misconduct charge and requested a paper hearing at which the Independent Regulatory Commission found proven the breach of FA Rule E3."
Ferguson was furious with Beck for not spotting Steven Caulker’s challenge on Wayne Rooney inside the Tottenham box when his side were already leading 1-0.
In his post-match interviews, Ferguson brought up Beck’s part in a goal awarded to Chelsea’s Didier Drogba at Old Trafford in 2010 that proved pivotal in that season’s title race.
"It was a clear decision. And he was 10, maybe 12 yards away from the incident and he doesn’t give it. And yet he gave everything else," Ferguson said.
"There was no way we were going to get a decision from (Beck)," Ferguson said. "We have got history with him.
"He never gave offside with (Didier) Drogba at Old Trafford when he was three yards offside. Everyone remembers that. I certainly do."
Ferguson subsequently claimed his criticism of Beck had been fair, and hinted the FA was pursuing a personal agenda against him.
"You never know the FA,” he said. "We are high profile and the profile of me is such that the FA naturally panic as soon as the press criticise them.
"I think that is what you will find. That is why they have sent me a letter. Whether I think it is unfair or not doesn’t matter to them really at this point. I just think it is more about me than what I have said."