The 71-year-old had denied the official charge on February 1, but has now been fined £12,000 for the disparaging remarks about Beck's "shockingly bad" performance following a decision by an Independent Regulatory Commission which included written evidence by the United boss.
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He said: "I think we should have had a throw-in down our side of the pitch but that linesman never gave us a thing all day.
"For me, it was a poor performance by him. He never saw the penalty kick for Wayne Rooney and some other decisions too.
"We remember him well from his time at the Chelsea game when Didier Drogba was three yards offside and he gave onside. I think he had a shocking game today, and I'm disappointed in his performance, I really am.
"I think he has had a bad game, and we never got anything from that side of the pitch. We got a bad break."