The Hammers have adapted well to life in the Premier League, while Southampton's return to the top flight has been dogged by a series of disappointing defensive displays.
Allardyce told The Mirror that even at this early stage of the season he considers picking up points against Saints to be of paramount importance.
He said: "It's almost a six-pointer this early in the season. If we win, they'd only have four points and we'd have 14 and that's a massive gap to try and close over the coming games.
"Southampton have not had the best of starts, with some difficult games and we have got to try to take advantage of that.
"Our fans intimidate the opposition and it is hugely supportive for us. That can help to give us extra drive to get the positive result."
West Ham have picked up 11 points from their first seven league games to secure a place in the top half of the table.