The Englishman made the comments following the Hammers’ 1-1 draw with Stoke City at the Boleyn Ground in the Premier League today.
Aaron Cresswell put West Ham in the lead as early as the seventh minute, but the London outfit conceded a late equaliser, as Marko Arnautovic found the target in injury time.
Allardyce was disappointed that his side failed to keep it tight at the back in the final minutes yet again and told BBC Sport: ”It's bewildering at the moment, since Manchester United we have thrown seven points away in the final seconds of the game.
“You tally those up, that's 50 points, looking good and its a really good season, but throwing this one away is bitterly disappointing.
"The lads showed a lot of nerves, and it was a very good goal from Stoke but it is difficult to take. We have to be more capable of seeing the game out.”
Over the course of 90 minutes, West Ham had just 35% of the possession, took 11 shots of which only three were on target, and earned four corners.
In contrast, visiting Stoke had 65% of the possession, took 18 shots of which two were on target, and earned 10 corners.
West Ham are currently ninth in the Premier League table with 43 points from 32 matches and are back in action on April 19 when they take on Manchester City away from home at the Etihad Stadium.