The 24-year-old has recently celebrated the birth of his son but has seen his side lose seven of their nine matches so far in the Premier League and occupy bottom spot having conceded 26 goals.
"Of course, after a game the adrenaline is flowing and I lie awake, thinking what else we could have done," Lallana told reporters.
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"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.
"I remember Saints [escaping relegation] time and time again. That shows there is always hope and we are only nine games into the season."