The Saints midfielder believes the club are moving forward under the Argentine following their 2-0 win over Reading, managed by ex-boss Nigel Adkins, at the weekend
The 2-0 win over Reading on Saturday, their third consecutive victory, took the Saints up to 11th in the table. Pochettino's side are now six points clear of the relegation zone with six to play, and Lallana admits that the controversial decision taken by owner Nicola Cortese has proved correct.
"We have progressed," Lallana told reporters. "We've got a different manager who's got a different culture about him and different methods and he’s gradually getting them across.
"It must have [helped us]. We're sitting higher in the league, we're scoring more goals and the table speaks for itself."
One player who has benefitted from more game time under Pochettino is striker Jay Rodriguez. The £6 million signing was a bit-part player under Adkins, but has made appeared more regularly under Pochettino.
The former Burnley man was influential in the win over Reading, grabbing a goal and an assist as the Saints denied their former manager a victory.
Speaking of Rodriguez, Pochettino added: "I am just really happy with him and all my players because they showed a great capacity to adapt to this new brand of football I want to play."