West Ham travel to White Hart Lane on Sunday for the first time since a small group of the club's fans shamed themselves by chanting anti-Semitic abuse in November last year.
Just four days after a Spurs fan was stabbed in an apparent anti-Semitic attack in Rome, a group of West Ham fans chanted "Viva Lazio" and "Can we stab you every week?" while some hissed, mimicking the gassing of Jews in the Holocaust.
West Ham warned their fans that any such behaviour at Spurs - who have a strong link with the Jewish community - would result in a banning order and potential criminal charges.
Allardyce echoed that warning on Friday morning, telling a press conference: "The club has made a statement so you will suffer the consequences if you do anything like that.
"If they do it, I think that's very important that they are identified and they suffer the consequences.
"We live in this society today so if you're made aware of what's acceptable and what's not you've got to be very, very careful about what you choose to chant. If you're made aware of it and it happens you don't have any excuse.
"My message to the fans would be: support the lads on the field and forget about everything else."
West Ham insist they do not tolerate racist or offensive language from their own fans.
And their statement on Friday spelled out the consequences for any fan who does not behave on Sunday.