Former Espanyol boss Pochettino replaced the sacked Nigel Adkins on 18 January and has led Saints to four wins in his 10 games so far, including a run of three victories in their last three games.
This has lifted the club to 11th in the Premier League table, six points clear of the relegation zone.
"We're sitting higher in the league, we're scoring more goals and I think the table speaks for itself," said Lallana, who scored Southampton's second goal in Saturday's 2-0 win over former boss Adkins' new side Reading.
"We've got a different manager who's got a different culture about him. He's got different methods and he's gradually getting them across to the players."
Lallana also praised striker Jay Rodriguez, who scored Southampton's first goal at the Madejski Stadium - the former Burnley man's third goal in three games and fourth in 10 since Pochettino's arrival.
"He's just flourishing under the new manager," added Lallana. ""I've always said he's going to be a big player and he's proving it now. He's unbelievable.
"There's no limit to where he can go. He's got all the attributes, physical and technical.
"The main thing is he's a top lad, got a great attitude, wants to do well for the team and it's a pleasure to have him at Southampton."
Pochettino is also delighted at the contribution of Rodriguez and predicted a bright future for the 23-year-old.
"He has a great dynamism, great technical quality and is obsessed by football, lives for football, has a great mentality and is always available," said Pochettino. "The sky is the limit for him. I don't see a roof, there is no limit."