Spurs star Danny Rose was allegedly targeted in the Three Lions' 5-1 Euro 2020 qualifying win, with Raheem Sterling and Callum Hudson-Odoi both addressing the issue post-match.
Ahead of facing Klopp's Liverpool on Sunday, Pochettino condemned the incident and, while offering his support to Rose, suggested the problem is far more widespread than football.
"[Rose] is OK," Pochettino told a news conference. "We wanted always from the beginning to show support, not only support to him but to Sterling and other people who feel [the abuse].
"We need to talk about how it's not only players, who we see easier, but people who feel the abuse every day in every single place in the world that we can't see and it happens every day.
"That's why I want to show support - of course to Danny and Sterling, but also for a lot of people who we don't know. It happens and they don't deserve to be abused. We need to fight against that, to try to stop that happening.
"In 2019, this situation still happening is something I can't believe and it's in our hands to do something to stop that.
"We need to apply our power to stop it happening. Nobody deserves to be abused and feel like Danny or Sterling or other people feel on the pitch and in the street."
Klopp also called for action, adding: "I don't know what to say about it really, because I'm so disappointed that at this moment, in our world, something like this is still possible, that people still use their voice for completely the wrong thing.
"It's so frustrating. I can't believe it.
"I watched the England game but without sound, so I was surprised when Hendo [Jordan Henderson] got a yellow card, when Rose got a yellow card, when Raheem celebrated in front [of the Montenegro fans]. 'What's going on there?' Then afterwards it makes sense.
"We're not allowed to ignore it. We have to point the finger, we have to speak loud about it, we have to finish finally that people are not allowed to do it. Maybe some guys who are doing it think it's funny - it's not funny.
"It's very difficult for me to really feel the situation of Raheem, of Rose, of our players who have faced something like that, because I've never had a situation like this. Whatever I could do, I would do.
"We have to stop games. I understand that Gareth [Southgate] didn't do it and say, 'come on, off the pitch' and stuff like that. But we have to make clear that that's not allowed and that's not possible.
"But there were a couple of incidents now in the last few weeks - not only racism, [also] running on the pitch and stuff like that. That's not fun. We have to make clear that that's not fun. Stop it."