The defender was shown a straight red card by referee Kevin Friend in the 36th minute of the 2-0 defeat, despite appearing to win the ball fairly from Charlie Adam.
Adam had already scored in the match by the time of Brown's dismissal and Steven N'Zonzi later doubled the hosts' advantage as Gus Poyet's men slumped to the foot of the Premier League table.
Sunderland told Perform on Monday that they had notified the Football Association of their intention to appeal.
The club's formal appeal must be submitted before 13:00hrs (local time) on Tuesday.
Sunderland, who have had four players sent off this season, will travel to Aston Villa for their next league fixture on Saturday.
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