Two goals in two second-half minutes from Dani Osvaldo and Rickie Lambert secured the Saints their first win at St Mary's this season.
The south coast side have already gathered 11 points from their first six games and this latest result means they sit above the likes of Manchester United, Manchester City and Liverpool in the table.
"We are very happy to get the first win in front of our fan and psychologically it's a big boost for us for the games ahead," Pochettino told Sky Sports.
"Football is a game played over 90 minutes and it doesn't matter when you score. We corrected certain things in the second half and we played our better football in the second half.
"The table right now doesn't count for anything at this moment.
"What will be really great is to finish the season in this position, but we have to believe we can do that.
"We have to believe that we can keep going forward and we want to keep working with the same imagination and bravery to do well."