The Tottenham ace made a silence gesture as he celebrated alongside Unai Emery's substitutes – which sparked a mass brawl of the sidelines.
Both of the clubs have been charged by the FA for failing to control their players during the North London derby.
But Pochettino has jumped to the defence of the England international and will not discuss the incident with him.
He said: "Look, to be honest, I didn't talk with him. Because when you do something and then it's so evident what happened after, you can take it in one or two directions.
"If you're a Tottenham fan, you take in one direction, if you're an Arsenal fan, you take in another direction.
"If you're the manager of Tottenham or Arsenal, or the Arsenal players doing the warm-up, you're going to back your players.
"There's no sense now to talk too much, now it's just to accept the FA charge or not. It's under investigation. If we did something wrong, it's normal to pay."
Dier's equaliser cancelled out Pierre-Emerick Aubameyang's opener before the Gunners bounced back to win the derby 4-2.
Arsenal fans trolled Dier after his deflection helped Alexander Lacazette's strike to find the back of the net.
Dier cheekily told Aaron Ramsey to "sit back down" during the celebration, but the Welshman hit back on Instagram after the match.
Pochettino, who raced down the pitch to try and diffuse the situation, has sympathy for the players involved.
He added: "It's difficult to control emotions in that moment.
"It's not easy. I was far away, I ran over, I arrived late and it was difficult to see what happened.
"I tried to watch on TV. It was difficult to control emotions, I think it's under investigation, the FA charge, and we'll see what is going to happen."
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