Despite the home side's best efforts, Villa held on for a point and could even have snatched all three at the death when Jussi Jaaskelainen saved excellently from Christian Benteke.
West Ham did have the best chances however, with Kevin Nolan, Ravel Morrison and Joe Cole going close in a relatively even game.
Allardyce, while disappointed to have to settle with the draw at home, was quick to look to the positives of a long-awaited clean sheet at home, following two consecutive defeats with three goals conceded in each to Everton and Manchester City.
"The amount of dominating play we had today, you're disappointed you didn't get three points," Allardyce told Sky Sports.
"In terms of territorial advantage and opportunities in Aston Villa's box we've absolutely dominated, but at the end of the day we still haven't converted that into goals.
"We're disappointed from that point of view but on the positive side we've got back to our clean sheet mentality at home."
Villa started the game perhaps the brighter, but the Hammers quickly found their bearings, to which Allardyce was happy.
"I felt we were going to score today and I think we got a little shaky start," he added.
"After 10 minutes we got settled down though, and we looked like we would get one or two.
"We've got to take the positives about stopping the defeats and getting a point on the board.
"We'll try and move on from there in the hope that, eventually, in the way we're playing both home and away, we'll convert that into three points."
With record signing Andy Carroll still in the treatment room with a heel injury, West Ham's forward line looks decidedly lightweight at the moment, though Allardyce was more than pleased with his side's forward play so far this season.
"There's enough quality balls in the box, but when we need somebody on the end of it we can't get it," he said. "What we couldn't find is the ultimate finish."
Allardyce was left to bemoan his injury-stricken side, however, with Carroll joined by the likes of Mladen Petric, James Collins, Alou Diarra and Matthew Taylor on the sidelines.
"We've got seven out I think, and a lot of those players are long-term injuries.
"Andy Carroll, we hope, is coming to the end so we can get him back, but we've got a few too many.
"That happens, though, so what we've got to try and do is get them fit and keep them fit.
"There's eight games in December for us, so we're going to need the squad fit and hopefully we'll continue playing the way we are at the moment."
Another positive Allardyce found was the home return of Carlton Cole, who re-signed with the club in the summer but has had his fitness questioned more than once since his arrival.
"Carlton's getting better and better. We went for three big strikers in the Premier League on loan but we couldn't get them, so we've brought Carlton and Petric in," he said.
"We are where we are with the strikers, and it's everybody else's responsibility to score as well. That's just eluding us at the moment."