The Saints impressed last season when Pochettino was surprisingly brought in to replace Nigel Adkins.
The Argentine guided them to 14th last term, but they have made a stunning start to the new campaign and are currently sat in fourth spot.
"We've had a full pre-season under him to get his tactics and methods across," skipper Lallana told the Daily Echo.
"You're starting to see all the rewards of our hard work under the manager."
Lallana admits the fans have soon been won over by Pochettino.
"It was normal for fans to think it was a strange decision, because Nigel Adkins had done a great job here," said Lallana.
"The fans' opinion quickly turned by the style of football and the way we were playing.
"There was an immediate difference, even in the first game against Everton.
"I wasn't fit at the time, I was watching, and I noticed it."
He insists that the club are not getting carried at the fact they are currently sat in a UEFA Champions League place.
"We'll just take it a game at a time," he said.
"For however long we're in fourth we're going to want to stay there and look up, we're not going to look behind us. That's the same as any team.
"We deserve to be there. We've been consistent. We've kept clean sheets.
"We're going to quietly go about our business."