The Saints are currently bottom of the table on goal difference, having been promoted from the Championship last season.
The South Coast club have the chance to move off the bottom when they face West Bromwich Albion on Monday night, but Lallana, who recently celebrated the birth of his son, admits that the team's performances have been leaving him sleepless at night.
"Of course, after a game the adrenaline is flowing and I lie awake, thinking what else we could have done," he said.
"We are coming into a run of games where we can get points, and we have to - it is just about tweaking a few things and getting that right result.
"In any case, I want to do well for my [son] Arthur, so when he grows up he will be watching the Premier League - not Championship football."
Saints take on the Baggies at the Hawthorns tonight.