Adam Lallana's first goal this season put Saints on their way on 19 minutes, after which the Welshmen went in search of a leveller only to be denied by some resolute defending and excellent goalkeeping from Artur Boruc.
Substitute Jay Rodriguez wrapped things up seven minutes from time to round off Saints' third consecutive league win and their fourth in all competitions.
The result lifts the hosts into the upper reaches of the Barclays Premier League table, leaving Pochettino proud of the manner in which the victory was secured.
"We scored early, and that put us into a pressurised situation because we knew that our opponents were going to try to get it back to one-all," he explained to Saints Player
at full time.
"We didn't play as well as we wanted to, but we got the result we wanted. We were able to withstand their attacks, so we've learned how to execute a certain phase of football today.
"We have to keep trying to establish how we want to play football, and I think we did that today.
"I am very happy for everyone involved with the club and all of the fans, but we've only just started – we need to keep working as hard as we are right now."
Pochettino had words of praise for captain Lallana, whose goal was his first since April: "He is a great player and a great guy," said the gaffer.
"He feels a lot of passion for the club. His performance today was fantastic, as were the rest of the players'.
"I am especially happy for him because he's been looking to score that goal for a long time. He worked so hard to make it happen, and today he took his chance. We're over the moon about that."
A number of players are now due to head off on international duty although one of those, Luke Shaw, is a doubt having missed today's game with tonsillitis.
"Luke may or may not travel because he has been ill," said Pochettino. "We'd rather he stayed with us, but we'll have to see how he progresses."