Mauricio Pochettino believes players should save their celebratory dressing-room videos and Instagram posts for trophy triumphs rather than mid-season league wins.
Pierre-Emerick Aubameyang shared a video of Arsenal enjoying their success after winning Sunday's north London derby, while an Instagram post from Aaron Ramsey appeared to mock Eric Dier, who sparked a first-half brawl when he celebrated his Emirates goal by putting a finger to his lips in front of the home side's substitutes and fans.
Defender Sead Kolasinac also posted on Twitter that Arsenal were the "K.I.N.G.S. of north London."
Pochettino last week praised his players' "humble" reaction to their own derby victory over Chelsea.
And, when asked on Tuesday how he feels about dressing-room selfies and crowing social media posts, he said: "Personally, I don't like it.
"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.
"In the end, Arsenal and Tottenham, we are on 30 points each. We're in a similar position, still with a lot of things to play for. But to be sporting enemies is a fantastic thing and I don't want to criticise what people want to do.
"Today it's normal. Look what happened in social media. I go with my dog to the park, Trent Park, and the most important thing [for other people] is not to share the walk with your dog, it's to share with your followers. I'm of the older generation. I accept the new technology but I try to keep a bit of that away."
Rather than being upset or irritated by the Arsenal players' revelries, Pochettino has taken pride from it.
"When people celebrate like this, it's because they respect you and see you as a big club," he said. "When we arrived here five years ago, the derby was a little bit 'well it's normally Arsenal always above Tottenham.' But now the last two seasons we were above [them], and how they celebrate, of course it's a derby but you start to see [those social media posts].
"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.
"[Our chief scout] Steve Hitchen was at the Liverpool game against Everton and was watching our game before in the stadium -- and when Arsenal scored the third goal all the Liverpool fans celebrated, like Arsenal celebrated after.
"It's clear we're doing something good. I love it when the people celebrate when they beat you. I don't like it when the people don't celebrate because it's normal to beat Tottenham."
Asked what Hitchen was doing at Sunday's Merseyside derby, Pochettino said with a laugh: "There is maybe a big surprise in January! He went to enjoy the entertainment, the experience."