Jay Rodriguez and Adam Lallana netted either side of half-time to lift Saints seven points clear of the relegation zone and heap the pressure on Reading.
Pochettino says he will not be letting his players relax as he wants them to enjoy a strong finish to the season.
"I felt today we played a very good game, but there are still a lot of points to be won," he said.
"Our goal is just the next game against West Ham.
"I am proud of what the players are doing. I think the club has brought me in to do a job and I am doing it well, so I am just pleased overall."
Former Southampton manager Nigel Adkins, now in charge of Reading, met Pochettino at the game and invited him for a drink after playing down any suggestions of ill feeling between the pair.
It is an invitation Pochettino confirmed he accepted, although he hopes Adkins will be providing the wine.
"I don't have to bring the wine - he invited me, no?" the Saints boss said.
"It is a tradition in England that I really admire and appreciate.
"I wished him all the luck in the world out there and told him it was a pleasure to meet him."