The former Espanyol boss took over from current Reading manager Nigel Adkins in January, and has since helped the Saints to four wins in his opening 10 games in charge of the club.
The last of these victories came on Saturday when the South Coast outfit beat the Royals 2-0 at the Madejski Stadium, and Lallana believes that Saints can move forward under the Argentine.
"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 the win over 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."
Saturday's victory has lifted the club to 11th in the Premier League table, six points clear of the relegation zone.