It ended a dismal run of three straight home league defeats for the Hammers but the West Ham faithful must be wondering if there is a curse this season at Upton Park.
Villa striker Christian Benteke came closest to breaking the deadlock when his second-half header struck a post, but that would have been an injustice in a match during which West Ham proved just how much they are missing injured striker Andy Carroll.
The Hammers have now gone 375 minutes without a goal at Upton Park and have scored just eight goals in 10 league games.
In truth, they have been an enigma so far this season. They have lost once and conceded just one goal in five matches away from home, the best away defensive record in the Premier League.
At home they started well enough with a win against Cardiff on the first day of the season but since then it had been torture for the Upton Park faithful.
This match was supposed to be Allardyce's line in the sand, the start of the home revival, and he drafted in midfielder Jack Collison for his first league start of the season in a bid to deliver some extra verve.
Collison formed a midfield triangle with Mark Noble and Matt Jarvis and there was no lack of zip or endeavour during a first half in which West Ham dominated possession and territory without seriously troubling Villa goalkeeper Brad Guzan.
Stewart Downing, playing against his former club and spraying passes around with some aplomb, jinked inside with the pace he once showed for England to drill a left-foot shot straight into the arms of Guzan.
And Jarvis went close when his direct running precipitated a frantic melee in the Villa penalty area, Jarvis rounding Guzan only for the goalkeeper to scramble back to block the shot.
Villa were content to do what they usually do best, play on the break.
It nearly paid off when Andreas Weimann broke through, only to have his shot blocked by the legs of West Ham goalkeeper Jussi Jaaskelainen.
But it was clear Villa were missing the injured Gabriel Agbonlahor. They lacked his searing pace to make their counter-attacking style effective, although Villa boss Paul Lambert clearly believed West Ham should have been reduced to 10 men after 15 minutes.
Ravel Morrison and Weimann tangled in a frantic foot race which ended with the Villa striker appearing to be hauled down when he was bearing down on goal.
Morrison was clearly the last man and if referee Howard Webb had not been generous in his judgement then Morrison would have seen red.
One of the main reasons for West Ham's impressive defensive statistics this season, however, is James Tomkins. He provides composure and organisation in the Hammers defence, one crunching tackle on Christian Benteke at the start of the second half perfectly illustrating his worth.
Yet for all the positives in West Ham's overall performance the bottom line is that they are struggling to score goals. They miss Carroll. That is obvious and Allardyce is desperate to get the injured striker back in harness.
Kevin Nolan is a willing worker and an intelligent play-maker at times but prolific is not a word which often enters his vocabulary.
Just after the hour mark Allardyce attempted to beef up the fire power, throwing on Joe Cole for Jarvis and Carlton Cole for Collision.
It brought a wave of West Ham attacks but Nolan squandered yet another chance when he stabbed his right-foot shot wide from eight yards.
But it was Villa who had the best chances, Benteke hitting a post with a header and then seeing a left-foot shot skew just wide after being deflected by a defender, although Joe Cole could have snatched it at the death if his shot had not been smothered by Guzan.
In the end, however, the result was probably fair. Neither side did enough to merit the three points.