Sead Kolasinac - who posted a victorious team picture from the dressing room - Pierre-Emerick Aubameyang and Aaron Ramsey were among the Arsenal players who took to social media after the game to rub the win in their opponents faces.
"Personally, I don't like it," Pochettino responded, as quoted by ESPN. "Obviously if you win a trophy, like I won when I was a player, it's a moment to celebrate. For me - this is my mentality and I don't want to say it's right or wrong - I love to celebrate in private and not make it public. I love to celebrate the things with your teammates.
"If you win, of course celebrate and show the fans you're happy - it's fantastic - but when you win a trophy, when you win something special."
Arsenal won the game 4-2 after scoring three unanswered goals upon falling behind, but it was still only enough to draw the Gunners level on points with their local rivals in the Premier League standings, leapfrogging them into fourth place by virtue of goal difference.
Pochettino is at least happy to believe that the reason for Arsenal's vibrant celebrations is because the Gunners now see Spurs as a genuine threat.
He added: "When people celebrate like this, it's because they respect you and see you as a big club...it was a massive win for them, of course, and for us it was a massive disappointment, but it showed the respect that we got in the last few years with our performances, with our results."