The FA said it would investigate claims of abusive chanting at the game while West Ham's Jewish co-chairman David Gold said the east London club would take a "zero tolerance" approach with any fans found to have made anti-Semitic taunts.
In a statement on Monday the east London club said five fans were arrested during the game and two cautioned by police for "racially aggravated gesturing", which media reports referred to as Nazi salutes.
West Ham are also working with London rivals Tottenham to identify fans heard taunting Spurs supporters, who have strong Jewish ties.
Visiting fans are alleged to have sung "Viva Lazio" and "Can we stab you every week?" in relation to the attack in which a Tottenham fan was seriously injured when a group stormed a bar in Rome where Spurs supporters were drinking ahead of a Europa League match with Lazio last week.
Media reports also said fans chanted "Adolf Hitler, he's coming for you" and hissed, mimicking the gassing of Jews during the Holocaust.
West Ham said the season ticket holder has been sent a letter containing a banning order from the club and that "any other individuals identified can expect a similar swift and robust response".
APPROPRIATE ACTION
"West Ham United will take the strongest possible action against any of their supporters, including enforcing life bans from the club, that are found guilty of behaviour which is categorically not condoned by West Ham United," the club statement added.
"During the 46 games in the Championship last season, West Ham United had zero arrests for racism or violence, so while we are surprised to see such reports today, we will examine any available evidence of such conduct thoroughly and take the appropriate action."
Gold, who took over West Ham with David Sullivan almost three years ago, was quoted by the BBC as saying: "David and I are leading an investigation from the top of the club to establish exactly what happened at White Hart Lane on Sunday.
"We have a clear stance towards any kind of discriminatory behaviour - it will not be tolerated.
"We will not let a minority of fans, no matter how small, affect the reputation of our great club.
"We are a club that promotes tolerance and inclusion of people from all backgrounds, race and religion. Just a quick look around our boardroom table would tell you that."
The FA has been battling a series of issues linked to racism, including banning former England captain John Terry for four games for racially abusing Queens Park Rangers defender Anton Ferdinand when playing for Chelsea last year.
Terry was cleared in a criminal case.
"The FA can confirm it has begun investigating reports of abusive chanting at the Tottenham Hotspur FC versus West Ham United FC fixture on 25 November 2011," the FA said.
"We note the statement issued by West Ham United FC and encourage clubs to identify and ban for life any individuals involved in incidents of abusive chanting.
"There is no place for anti-Semitism or any form
