Moyes was sent to the stands at Southampton in the League Cup last week after referee Chris Kavanagh waved away a late penalty appeal.
The former Everton and Manchester United boss, whose side are bottom of the Premier League with only two points from 10 matches, later admitted that he had deserved to be banished from the touchline after swearing at the fourth official.
"The problem was he chased me down the touchline. I swore at him and I shouldn't have done so," the Moyes said at the time.
Moyes, whose side were beaten 4-1 at home to Arsenal on Saturday, was also fined 8,000 pounds.
(Reporting by Toby Davis; editing by Martyn Herman)
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