"Arsenal and Tottenham Hotspur have been fined 45,000 pounds and 50,000 pounds respectively after both clubs admitted an FA charge of failing to ensure their players conducted themselves in an orderly fashion," the FA said in a statement.
Gabon striker Pierre-Emerick Aubameyang's brace and strikes from Alexandre Lacazette and Lucas Torreira had helped Arsenal cancel out goals from Dier and Harry Kane to win the match.
The ill-tempered contest saw a banana skin thrown on to the Emirates Stadium pitch by a supporter after Aubameyang scored. Tottenham later promised to ban the culprit.
The Metropolitan Police then charged four men after incidents during the match.
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Wednesday's League Cup quarter-final meeting between the two teams was also mired in controversy after Tottenham's Dele Alli was hit in the back of the head by a plastic water bottle shortly after he scored their second goal in a 2-0 win.
Arsenal said on Thursday they have identified an image of the individual who threw a bottle at the Emirates Stadium and are working with police to apprehend the suspect.
($1 = 0.7913 pounds)
(Reporting by Shrivathsa Sridhar in Bengaluru; editing by Martyn Herman)
