Magpies goalkeeping coach Andy Woodman and Saints counterpart Toni Jimenez were both sent to the stands after a pushing match between the two benches following substitute Morgan Schneiderlin's rugged injury-time challenge on Massadio Haidara.
Pochettino: "What happened at the end of the game is not a good example, it's not good for football.
"From our point of view, we are going to try our best not to let it happen again because it's not good for anyone and not good for the sport.
"I think it is avoidable but also in a high-intensity game such as that, any little spark can lead to something else and I think that's what happened.
"From our point of view, it's something that we regret and that we don't want ever to happen again.
"Let's stay calm, we need to be calm about what happened today. These things can happen and we need to keep it indoors, not publicise it and make a big thing out of it."
Opposite number Alan Pardew insisted the incident should not be allowed to overshadow a hard-fought encounter which both teams had chances to win.
Pardew: "It was a bit of panto season. I'm not going to get carried away with that because it shouldn't take the headlines.
"The battle is on the pitch and that was a terrific battle. The one on the sideline was pretty pathetic, what I saw of it, and best forgotten.
"I had my back to it most of the time. I just said to their manager, 'Just get your staff in, I'll get my staff in and let's get on with it because we want to win the game', and he was of the same opinion as me."