The Hammers have now lost their last four games in a row following Saturday's 1-0 defeat at West Bromwich Albion.
With two fixtures left to play this season, West Ham need just a single point to confirm their top-flight status for the next campaign.
"[Failing to score] has been our real Achilles heel in that bad turn of results we've had," Allardyce told the club's official website.
"While performances might be seen to be up there and we are creating chances, we're not winning football matches at the moment and we're not even drawing them and that's of huge concern for me.
"At the other end, when we used to be so solid defensively we don't seem to be quite so solid as we were. We haven't had a clean sheet for a long time and having got 13 clean sheets up until the last six games, just one clean sheet would give us enough points to start planning for next year."
West Ham return to Premier League action on Saturday when they welcome Tottenham Hotspur to Upton Park.