The Italian's frustration boiled over at the final whistle following the 1-0 loss and he confronted referee Darren England in the tunnel.
After the match, De Zerbi said the standard of referees in the Premier League is "very bad".
"... Roberto De Zerbi has been suspended from the touchline for one match and fined 15,000 pounds...," the FA said on Friday.
"The head coach admitted that his behaviour on the pitch at full time was improper, and that his behaviour and/or language in the tunnel afterwards towards a match official was abusive and/or insulting and/or improper."
Later on Friday, De Zerbi told reporters: "I think I didn't make mistakes in terms of respect.
"The players know what to do. I am lucky to be a coach of this squad. It is not a problem for them if I'm not on the bench, although I prefer of course to stay on the bench. It is my life."
Brighton, who are eighth in the league standings, host 16th-placed West Ham on Saturday.
