A section of West Ham fans mocked the stabbing of a Spurs fan in Rome during Tottenham's 3-1 victory over their London rivals at White Hart Lane on Sunday. A group of away fans were heard hissing, mimicking the sound of Jews being gassed during the Second World War, and also chanted the name of Adolf Hitler.
Hammers boss Allardyce told a press conference on Tuesday: "I don't view any type of chanting (of that nature) to be allowed or accepted in the game of football today. I think that fans who are next to these people should deal with them first and foremost if possible."
Allardyce added: "The West Ham fans are absolutely fantastic with the support they give us and then you've got this small minority that are creating this sort of ill-feeling towards the vast majority of West Ham fans."
Tottenham manager Andre Villas-Boas, like Allardyce, was reluctant to condemn the chanting in the immediate aftermath of the game as he said he had not heard it. Having studied the footage of the game for the last 48 hours, Villas-Boas has been left in no doubt as to the nature of the chanting that was coming from the away end.
"The level of aggression of the chanting goes out of proportion. It is complete stupidity," the Tottenham manager said. "I am grateful for the quickness in which both clubs have gone into the matter, plus the FA and police.
"I think West Ham have set an example immediately by giving a lifetime ban on the fan. It was obviously avoidable and I am pretty happy with the way that both clubs have worked with each other to try and get the actions right immediately."
West Ham have banned one fan for life because of the chanting and two supporters were cautioned by police for a racially aggravated public order offence. Allardyce has no doubt that should there be any more culprits out there, they will be caught.
When asked if supporters found guilty of such abuse should be banned for life, the West Ham boss said: "Yes. It's a small minority but at the end of the day a small minority can make themselves heard at football matches if they really want to and we must deal with it.
"The good thing is with security cameras and CCTV cameras, it's difficult for them to get away with it. Hopefully we can pick out those people and punish them in the right way."