The Hammers, fresh off a 3-1 win over West Bromwich Albion last week, held the Reds to a 0-0 draw on Merseyside to push them up to 12th and six points clear of the relegation zone which delighted Allardyce, particularly from a defensive viewpoint.
"To have won would have been a massive bonus for us as it is 50 years since we last did it," said Allardyce.
"But it is still a very big point, and very well deserved.
"I don't think we have defended better away from home all season.
"(James) Collins and (James) Tomkins were really good when you consider how few chances Liverpool had."
Regarding West Ham’s chances of staving off relegation, Allardyce added: "I'd like another three points.
"It depends on the run of the teams below us because some are picking up two or three wins back to back. But we are looking up, not down."