Both managers were the victims of abuse from the spectators, as well as former Gunners frontman Emmanuel Adebayor, who recently crossed the north London divide by joining Spurs on loan from Manchester City.
The club confirmed that several spectators were ejected from the stands during the game from both the home and away sections of White Hart Lane.
"It is club policy to ban fans who are found guilty of abusive chanting," a Tottenham spokeswoman said.
The club have also released a statement on their official website appealing for information, and said they would work closely with Arsenal to identify culprits.
"Both clubs were extremely disappointed to hear the chants from supporters at yesterday's game," the statement reads. "Neither club tolerates foul language, racist chanting, homophobic chanting or any anti-social behaviour from its supporters. We shall be working closely with each other to identify the individuals involved.
"We should like to remind all of our supporters that we do not tolerate discrimination of any sort at the club, on the pitch or in the stands. If you experience any form of discrimination, help us to eliminate it from football."
The statement adds: "We have a fantastic atmosphere at the Lane and by working together we can prevent the small minority ruining it for everyone."
Meanwhile, Harry Redknapp revealed his disgust at chants aimed both at him and Adebayor, insisting that the perpetrators "need help".
"What was chanted at Emmanuel was disgusting," Redknapp said. "There was some pretty disgusting chanting at me as well but that's life. How do you chant something like that at someone? You can't be right mentally. You need help.
He added, "It's got no place anywhere in life. Emmanuel never said anything to me [about the chants]. I think he regretted what happened when he ran to the Arsenal fans after scoring for Manchester City the other season."
Redknapp defended Adebayor's actions after having a first hand look at the abuse the striker had to take from Gunners fans.
"Even then what did he really do? They are all shouting abuse and he ran up and said 'have a bit of that'. It might have been a bit over the top but he'd been getting grief for 80 minutes and that's how he reacted."
Arsenal manager Wenger was asked if he disapproved of the chanting from both sections of the support, and said,"Yes. We respect everybody and want to be respected as well."
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