The home side moved in front as early at the seventh minute on Saturday, when Aaron Cresswell's magnificent free-kick left Asmir Begovic clutching at thin air in the Stoke goal.
But the Potters took advantage of some nervy home defending to snatch a point right at the death and leave Allardyce exasperated.
"It's bewildering at the moment," he said.
"Since [conceding a late goal to] Manchester United [in February], we have thrown seven points away in the final seconds of the game. That's against Spurs, Leicester [City] and Stoke today.
"You tally those up, that's 50 points [that West Ham would have, which would have been our greatest points total ever in this league and it looks like a really good season.
"So throwing this one away is bitterly disappointing. The lads showed a lot of nerves and brought a little bit of panic into what we were trying to do and while I have to say that it was a very good goal from Stoke, we should have dealt with it well before it went in.
"We failed miserably to do what we needed to do in the last few seconds. We should have kept possession much better in the moments before that goal and we have to be more capable of seeing the game out."
The two sides began and ended the day locked on the same number of points in mid-table and there was little to choose between them in a hard-fought clash that contained enough goalmouth action to keep a crowd of nearly 35,000 entertained.
Unfotunately for West Ham, however, Enner Valencia was forced to limp from the fray in the second half having returned from a month-long absence with a toe injury, while fellow frontman Diafra Sakho also went off injured.
The pair have contributed 14 league goals between them this season and Allardyce was understandably dismayed at the prospect of both men missing next weekend's trip to Manchester City.
"Goals are going to be harder to come by because we lost those two strikers," he said.
"Sakho has a thigh injury and Valencia hobbled off after a kick. He wasn't going to play the whole game anyway because he's only just back from injury.
"And we've got Andy [Carroll] out until next season, which means we've got to be even more resilient because we're going to score even fewer goals if those players are missing.
"If it's more than a grade one tear with Sakho, we'll be lucky to see him again this season. It's a blow because he's our top scorer, but we'll just have to deal with it."
