Newcastle were the better side in the first half and went in at the break ahead, courtesy of Yoan Gouffran's goal after a mistake by Jos Hooiveld.
However, Southampton improved in the second half and deservedly drew level thanks to a superb effort on the counter attack from Jay Rodriguez.
Pochettino had no complaints with the result, admitting it was a typical game of two halves.
"I think overall in the analysis of the 96 or 97 minutes played the draw was a fair result," said Pochettino.
"Perhaps we could have even got something a bit more from this game.
"I think both halves were completely different.
"In the first half it was wide open and both teams were creating good chances for themselves.
"I think in the second half Southampton was completely dominating the game and could have gone on to win.
"The overall analysis is the draw is a fair result."
The game was marred late on by a scuffle involving both benches as Southampton goalkeeping coach Toni Jimenez and his Newcastle counterpart Andy Woodman were sent to the stands for their part in the melee.
Pochettino was disappointed with the brawl and is determined not to see the scenes repeated.
"I think what happened at the end of the game is not a good example. It's not good for football," admitted Pochettino.
"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, 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.
"Overall from our point of view it's something we regret and we don't want ever to happen again."