Wenger was frustrated by the timekeeping of the match officials
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He will miss Tuesday’s Carling Cup tie at Tottenham after his actions at the end of Saturday’s draw with Sunderland.
An FA statement read that Wenger “admitted a charge of using insulting and/or abusive language and behaviour”.
Wenger appeared to confront fourth official Martin Atkinson after Sunderland scored in stoppage time.
The 60-year-old was unhappy that Darren Bent‘s strike came in the fifth minute of injury time after Atkinson had signalled a minimum of four minutes would be played.
Victory would have taken the Gunners to the top of the table.
Wenger could have appealed against the FA‘s charge, which would have freed him to take his place in the dugout at White Hart Lane.