Spurs had trailed 1-0 following Pierre Emerick-Aubameyang's early penalty but hit back through Eric Dier's headed equaliser.
Dier's exuberant celebrations in front of the home supporters prompted a furious reaction from several Arsenal substitutes, leading to heated clashes on the sidelines, which Pochettino raced to intervene in.
"At 1-1 there was a massive fight, but I didn't know what was going on," he said.
"When I arrived it was all relaxed and calm.
"In that moment when you score the energy is on your side. To keep that energy, you need to be clever in that moment.
"It's okay to celebrate and then go back and try to continue to play."
Harry Kane put Tottenham ahead soon after order had been restored, but Aubameyang's stunning 56th-minute leveller set Arsenal on their way to a turnaround of their own. Alexandre Lacazette and Lucas Torreira completed the comeback before Jan Vertonghen's red card ended any slim hopes of another Spurs comeback.
While not having any complaints with the Belgian's dismissal, Pochettino did have some sympathy with his defender.
"I think it was a little bit unlucky," he added.
"When you run to the ball, how do you stop the run? You want to touch the ball and it was so quick how Lacazette arrived.
"Of course, it was a dangerous action. In that moment it is maybe a yellow or red card. It is how the referee assess it.
"It was dangerous, but it was a little unlucky because he touched the ball first."