In-form attacker Son Heung-min was responsible for two of the goals on the south coast, taking his tally to seven in four matches and earning particular praise from his manager.
Pochettino told Sky Sports News: "The answer today was perfect after Wednesday. We conceded the first goal. It is always tough to play here but after a few minutes the team managed to complete the game with a big victory and it is important because it put us in an important position in the table.
"It was a fantastic performance today from Son. Football is about the squad, not only about the 11 players who play. In 10 months of competition everyone is an important part of the project and fighting for the same objective.
"There is still a lot of work to do, still a lot of things can happen with eight games to go. Big sides are fighting with us to take a position in the top four."