One Arsenal fan appeared to make an anti-Semitic gesture in the direction of Spurs fans in a video.
Another fan was ejected after allegedly chanting about 'gassing Jews'.
Dele Alli was also injured after being struck by a bottle thrown from the crowd.
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The player did not appear hurt and turned to the crowd and used his hands to gesture the scoreline to them.
"We have all been embarrassed by the individual who threw a bottle at Alli," Arsenal said in a statement.
"Behaviour of this type has no place at Emirates Stadium and after analysing CCTV footage, which showed him leaving the stadium after throwing the bottle, we have identified an image of the suspect.
"We are liaising with the Metropolitan Police and investigations continue to apprehend the culprit. We are not responsible for the actions of one individual, but send our apologies to Alli and everyone at Tottenham."
The club said in a statement released to British media that it was aware of the alleged incident of anti-Semitism and investigations were ongoing.
Tottenham have historically had a substantial support base among London's Jewish community and fans of the club have been targeted by some rival fans with anti-Semitic chants for years.
Arsenal stressed they would not tolerate any anti-social, discriminatory or violent behaviour and urged supporters with information that could help identify the accused to come forward.
"Anyone identified will receive a lengthy club ban and their details will be passed to police to commence legal proceedings," the club added.
The Metropolitan Police had charged four men following incidents in the North London derby between Arsenal and Tottenham this month.
A banana skin was thrown on to the Emirates Stadium pitch by one supporter after Arsenal's Gabonese striker Pierre-Emerick Aubameyang had scored in the 4-2 win.
Tottenham said the supporter would be banned from matches.
London rivals Chelsea banned four supporters this month pending a police investigation into alleged racial abuse of Manchester City forward Raheem Sterling in the sides' league fixture.
More embarrassment followed for Chelsea after UEFA launched an investigation into allegations of anti-Semitic chanting by their supporters during their final Europa League group match against Vidi FC in Budapest last week.
The Premier League acknowledged that a number of fans had behaved "unacceptably" at matches and urged supporters to conduct themselves in a respectful manner.
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