The Saints brought the Reds' unbeaten start to the season to an abrupt halt as they left Merseyside with a 1-0 victory.
Mauricio Pochettino set his side up to press from the front, preventing Liverpool from playing their way out from the back.
He got his tactics spot on, with Liverpool drawing their first blank of the campaign as they toiled for long periods.
Lallana said afterwards: "They are a team like us who like to play out from the back and we just played a high-pressing game and felt we won the ball back in areas where we could affect the game.
"We wanted them to play it long.
"It's credit to the staff, the players and everyone who works at the club.
"We worked hard on our game plan all week and we executed it brilliantly.
"The last 10 or 15 minutes get a bit edgy when you're winning. You tend to drop off a little bit deeper and people get tired. But I don't remember them having a serious chance."