Allardyce: No issue with defensive formation
The stalemate left West Ham with only eight goals from their 10 Premier League matches so far this season, and having taken just a point from their last four home league games.
But Allardyce, whose side are now 14th in the table, two points above the relegation zone, nevertheless chose to accentuate the positives.
"We tried our very, very best to get that all important victory, but one of the most important things was making sure we didn't suffer another defeat, and our defensive unit was magnificent, apart from one situation when (Christian) Benteke got in with the header that hit the bar," the West Ham boss said.
"So we've limited Aston Villa to one chance in the whole game. We've limited them to eight crosses only into our penalty area and we've put 38 balls into the opposition's box.
"It’s all about somebody putting the ball into the back of the net when you get so many opportunities, and unfortunately that's our Achilles heel at the moment."
That is also a situation that owes much to a series of injuries to West Ham's forwards.
Andy Carroll, the club's record signing, is expected to be out of action for another month, while Ricardo Vaz Te and Mladen Petric are also on the sidelines.
Carlton Cole, who came on as a second-half substitute against Villa, is short of match fitness after being without a club for five months before his recent return to Upton Park, and Allardyce has seemingly lost faith in Modibo Maiga.
On the latter he added: "He has had several, several opportunities to stake his claim this season and unfortunately hasn't scored."
That striker conundrum has left Allardyce operating a controversial 4-6-0 formation, but the 59-year-old former defender is adamant that the lack of a striker in his line-up is not the cause of West Ham's current scoring troubles.
"That's not the problem," he said. "The problem is that our goals were shared out last year. All the players in our team scored. There was only Guy Demel of the first 16 or 17 in our squad who didn't score a goal. Kevin (Nolan) got 10, Andy (Carroll) got eight, and everybody else got two, three, four, one. That's why we finished 10th.
"At the moment, none of those players in the team are scoring a goal when they get the opportunity like they did last year. It's all the players not contributing in goalscoring terms as much as they did last season. And if we get that right, which I think we will, then we'll start getting three points instead of one."
West Ham have only seized maximum points once since the opening day - a 3-0 victory at Tottenham last month - and they will get the chance to arrest their slide when they visit third-bottom Norwich next Saturday.