The incident in the 95th minute of the match was missed by referee Lee Probert, but was caught by the FA after a review of video evidence.
Gomes will miss Everton's league games against Manchester United, Crystal Palace and Burnley.
The 25-year-old will be eligible to return for the Merseyside club against Tottenham Hotspur on the final day of the league campaign on May 12.
(Reporting by Hardik Vyas in Bengaluru; Editing by Toby Davis)
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