The Upton Park club have drawn a blank in their last two Premier League games, drawing with Newcastle United and losing 1-0 to Stoke City, having opened the campaign with a 2-0 victory over newly promoted Cardiff City.
Allardyce was heavily critical of his men after the home loss to Stoke last time out and he has demanded an improvement.
"I'm looking for us to give the kind of performance we gave at Newcastle and this time be more clinical," he 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.
"We must perform to the level we did at Newcastle and take our chances, because if we don't it will be a very tough game, because we've seen the improvement they've made."
West Ham scored 45 goals last season, two fewer than relegated Wigan Athletic.
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