Pochettino told BBC Sport: "Always in football to get three points you need to work hard. It was difficult, tough. In the end we were better and deserved to win.
"First half we played very well. Second half we conceded a goal with our mistake and we allowed Southampton to score. It is another victory, we remain in second position and we have reason to be happy.
"The aim is the next game. We have 10 days without our players we hope nothing happens and all will arrive in good position."
Spurs return to action after the international break with a Premier League trip to Burnley on April 1.