Dejan Lovren's header from a 53rd-minute corner gave the visitors their first win since the opening day of the season, ending leaders Liverpool's unbeaten start to the campaign in the process.
And Southampton boss Pochettino expressed his delight at the way his side performed.
"We were outstanding," he said.
"We're very pleased and satisfied with the performance; we played very well at a tough ground.
"Especially in the second half, we were superior and we played how we wanted to.
"It's not easy to come here and win so we're really happy and all the players need to be congratulated for a great performance.
"Overall we were faithful to our philosophy, over 90 minutes we were superior and we were able to capitalise on our chance and take the win."
Pochettino was especially pleased with the way his men reacted in the second half after their hosts had arguably had the better of the first.
"In the second half we came out and corrected what we hadn't done," he added.
"We have to learn from these games and the experience. We were too defensive in the first half. We pressed higher and got on the counter attack (in the second half).
"We fully believe in how we want to play and a victory like today reinforces that belief even more."
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