Spurs ran out 2-1 winners at White Hart Lane but the game was overshadowed by chants aimed towards former Gunners striker Adebayor.
Despite the chants, Adebayor impressed for his new club, setting up Rafael van der Vaart for Tottenham's opener before Kyle Walker hit the winner following Aaron Ramsey's second-half equaliser.
Redknapp admits he was outraged to hear the songs.
"It was disgusting, yeah, disgusting," the Tottenham boss said.
"There was some pretty disgusting chanting at me but that's life.
"How do you chant something like that to someone?
"You can't be right mentally. You need help.
"There are kids up there as well.
"It's got no place anywhere in life, that sort of stuff."
There was also controversy following the final whistle when Clive Allen clashed with Wenger after the Spurs coach felt the Gunners boss had snubbed his offer of a handshake.
Wenger squared up to Allen and both had to be restrained before the Frenchman disappeared down the tunnel.
Redknapp admitted Allen was unhappy at the apparent snub.
"I think Clive went to shake hands with him and he missed Clive - he didn't see him," Redknapp said.
"You either shake hands and mean it or you don't shake hands at all.
"If he doesn't want to shake hands, it's his prerogative.
"I think he (Allen) wasn't happy."
Arsenal dominated the first half but missed a host of chances before Van der Vaart fired home to put Spurs ahead.
The game seemed destined for a draw after Ramsey's tap-in put Arsenal back in it but Walker then sprung a surprise by hammering a 30-yard bullet that beat Wojciech Szczesny.
Redknapp was delighted to have achieved his third win over Arsenal as Spurs boss.
"Obviously, it's great for the fans to beat Arsenal and it's a big game," Redknapp added.
"When you've beaten one of the teams that are going to be up there challenging with you, it's always a bonus.
"We certainly knew we're going in with a big chance of winning."
When asked what happened with Allen, Wenger said: "Nothing. I shook the hand of the manager and the assistant manager. How many people do I have to shake hands with? Is there a prescription? There were no words exchanged."
Wenger's team have now lost four of their opening seven games and sit 15th in the Barclays Premier League table.
The Frenchman was defiant after the final whistle, however, claiming that Spurs' first goal should not have been allowed to stand because Van der Vaart handled the ball before unleashing the volley that put the hosts ahead.
He said: "It's frustrating because the first goal was handball and I wonder what the linesmen do in these situations. It's a second yellow card as well, because he already had a yellow card."
Gervinho, Arteta and Theo Walcott were all guilty of missing chances in the first half - something which clearly annoyed the Arsenal boss.
"We played with the handbrake on in the first half," he said.
"But at half-time we came out and had a go at them and normally got back to 1-1.
"But then we didn't push on enough and let them get back into the game. That shows we are not playing with confidence at the moment. We want to protect our result too much when we have one."
Tottenham full-back Walker admitted "it doesn't get much better than that" after his winner.
He told Sky Sports 1: "It doesn't get much better than that. I just picked the ball up and hit it.
"I had one of them against Fulham for Aston Villa so I thought why not take a chance.
"I just thought why not have a go. If you don't buy a lottery ticket you don't win the lottery.
"Arsenal are a good team and we found it difficult at times but we dug deep and got the result that we wanted."