Jose Fonte scored the only goal of the game 21 minutes from time to extend the Saints' unbeaten top-flight run to six matches and move them up to eighth, with the Argentina always confident of taking three points even at 0-0.
Pochettino told reporters: "I think the victory is fully deserved. On a tough pitch against tough opposition, we were fully superior to Hull.
"[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.
|13/2||Southampton are 13/2 with Bet365 to beat Sunderland 1-0 in the FA Cup|
Hull defender Paul McShane was an injury concern after being stretchered off after 12 minutes following a collision between himself, Rickie Lambert and Allan McGregor.
The Republic of Ireland international has not broken his ankle, however, Steve Bruce confirmed, though a lay-off is still to be expected.
"We have seen the X-rays and they revealed that there is no break but I don't know if you have seen it like I have," he Tigers boss explained to the press. "The video evidence doesn't look great - his ankle was in a horrible position so we fear ligament damage. Until we see the scans [on Wednesday] we are unsure but it doesn't look good.
"We now have to just dust ourselves off and get ready for our cup game at the weekend [against Brighton & Hove Albion]."
Bruce described Southampton as an "excellent" side after seeing his team drop down to 13th in the table, cconceding that Pochettino's men were by far the better team in a game where the hosts rarely threatened to score.
"Southampton are the best of the so-called smaller teams," the Hull manager remarked. "If you take away the big boys then they are the best team and they made life very difficult for us.
"The best team on the night won; we had to be at our best and we weren't. We surrendered possession and went back to front far too quickly, which is not like us.
"Fair play to Southampton, they put us under pressure in the midfield areas and they were excellent. Sometimes you just have to hold your hands up and say you were beaten by the better team."