It was the latest of several impressive performances from the Saints skipper, who manager Pochettino believes could well be next in line to represent England.
"I'm very happy for Adam," he said of Lallana, who was called up for England's World Cup qualifier with Ukraine in September 2012 but did not play.
"He's a great bloke and a great professional and he's very passionate about this club, about Southampton, so I'm happy for him.
Pochettino also heaped praise on goalkeeper Artur Boruc, who pulled off a string of fine saves as Southampton recorded a fifth clean sheet of the season.
"He was incredible," Southampton boss Pochettino said of the Poland international. "He did ever so well, but it just shows we have full trust in his performances and his skill, and also in our other keepers.
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Further heavy showers gradually clearing away this evening. Dry but chilly tonight, then dry with plenty of sunshine tomorrow.
Heavy showers turning potentially thundery this afternoon. Becoming dry but chilly tonight, then dry and sunny tomorrow.