A section of Hammers' supporters appeared to mock the gassing of Jews in the Holocaust during the Premier League clash at White Hart Lane, which Spurs won 3-1.
The pair of fans were arrested during the game and accepted the police cautions, Scotland Yard said.
Tottenham Hotspur have a large fan-base from the Jewish community and the north London club has historical Jewish roots. The abuse came four days after Spurs' fan Ashley Mills was stabbed in an attack by Italian hooligans before Tottenham's game against Lazio in Rome.
West Ham said it would take "the strongest possible action".