Allardyce's men stretched their unbeaten Premier League run to five matches but were denied a sixth top-flight win of the campaign by a fine showing from Villa goalkeeper Brad Guzan at Upton Park.
The American made numerous saves to keep the hosts at bay, with his flying one-handed injury-time stop denying striker Andy Carroll – making his first appearance since May – a dream return to the side.
Despite expressing satisfaction with his team's overall performance, Allardyce could only lament their failure to beat Guzan.
"It was a terrific effort that we gave," Allardyce said. "It goes down to the strength in depth of the squad.
"When we lulled a bit in the second half, the changes - one, in system and two, in personnel - gave us that more exciting, all-important finish that gave our players and our fans the biggest chance to see another win here.
"The sad thing is that when our finishing was very good, the goalkeeper was even better, and some of the time I was a little bit disappointed in our finishing considering how good we've been this season.
"We've got to respect the point, it's our second clean sheet [of the season] which is good. Everything the lads did today around how Aston Villa played, they did very, very well.
"We broke them down several times apart from we couldn't break down the keeper today.
"Before Andy [Carroll] came on Diafra [Sakho] had two free headers in the box and they've gone over the bar. We had a couple of shouts for a couple of penalties that didn't go our way but that shouldn't have mattered for us today with the amount of chances we've created.
"We are a little frustrated but we couldn't do any more than we've done."
