The Hammers will head into the match having failed to score in their previous two outings, the last of which was a 1-0 defeat at home to Stoke City.
"I'm looking for us to give the kind of performance we gave at Newcastle and this time be more clinical," Allardyce told the club's official website.
"We've gone two games without scoring a goal now, which is something I don't like, even though we've been very good defensively.
"We need to be putting the ball in the back of the net more, so when a chance comes along at Southampton we must take it."
West Ham are currently in eighth place in the Premier League table.