Jose Fonte scored the only goal of the game 21 minutes from time to extend Southampton's unbeaten run in the top flight to six matches and move them up to eighth in the league.
Pochettino believes his players were the better side at the KC Stadium, adding that he was always confident of taking three points even at 0-0.
"I think it's fully deserved, the victory is fully deserved. On a tough pitch against tough opposition, we were fully superior to Hull," he said.
"(Hull are) a team that have invested quite a bit during the transfer window and I think overall, with the performance of the team, we fully deserved the three points.
"We always had the hope and I think we showed the capacity to have the patience to look for the goal and in the end we achieved it.
"We kept on searching for the goal and overall we played how we play, how we always play and in the end I think the goal was fully deserved it and the victory as well."
Southampton travel to West Ham next in the Premier League on Saturday with the sides having drawn 0-0 in September's reverse fixture.
