Christian Eriksen drove home an effort five minutes before the break at White Hart Lane as Tottenham picked up their first win in five Premier League outings.
And Pochettino, who swapped the English south coast for north London during the close-season, recognised his players' efforts in overcoming an opponent he knows all too well.
"It is an important win," he told BBC Sport. "It was a very tough game. Southampton have unbelievable players.
"We are still improving. I arrived three months ago. It is always difficult to put together a different philosophy in such a short time. It is important to build something for the long term.
"All the players did a great job today and did their best. We deserved the three points."
Despite ending his former employers' seven-match unbeaten run in all competitions, Pochettino stressed that he still held Southampton in high regard.
"I love Southampton and the club," he added. "It was a great period. Southampton will always be special for me in my heart."
