The Hammers defended resolutely at Anfield and restricted Liverpool's opportunities, even going close to snatching all three points late on when Jack Collison saw a header cleared off the line.
Allardyce was pleased with the gutsy performance of his players and even felt they might have done enough to nick all three points.
"It was very, very good indeed," he told Sky Sports.
"I think when you frustrate the opposition and you keep the Anfield crowd quiet then you know your team is doing something right.
"And then when you take your possession, which is obviously going to be limited against Liverpool, and create as much as we did today too.
"I am absolutely delighted with the point but also a little disappointed we didn't win this game today given the clear-cut chances that fell to us and not to Liverpool."