Spurs beat their rivals on Sunday afternoon courtesy of a 2-0 scoreline which was enough to mathematically secure a higher league position than their rivals for the first time since 1995.
Emotions ran high during the game, with Spurs determined to claim bragging rights over Arsene Wenger's side before bidding farewell to their famous old ground.
But excitement got the better of Pochettino, who is no stranger to touchline passion, as he celebrated Alli's opening goal against the Gunners.
The Argentine coach struck his assistant in a bizarre incident and joked he had been inspired by Anthony Joshua's epic heavyweight battle against Wladimir Klitschko
"Look how he's red," Pochettino told Tottenham's official website while pointing to a mark behind his colleague's ear.
"After the goal I jumped and 'punch!' It's because yesterday I was watching Joshua and Klitschko!"
"It was a fantastic afternoon. I'm so pleased and happy for the players and for our fans. It was so emotional for everyone."
Spurs are now four points behind pacesetters Chelsea with just four games left to play.
And Pochettino is adamant that the Lilywhites' focus should be on catching Antonio Conte's side rather than revelling in outdoing Arsenal.
"I am so happy but our aim is to challenge and win, not only Arsenal but the other 19 teams that play against us in the Premier League.