The Hammers boss said that he was pleased with their defensive display, but urged his players to build on the solidity with more potent attacking performances in future.
Allardyce told Sky Sports News: "We were not at our best today. In possession we made life extremely difficult for ourselves. We never got the crowd excited and we never got quality balls into their penalty area.
"I point to the one side that we have done well in this season, and that is our defensive work. We have eight clean sheets already this season and we have built our base superbly.
"What the lads need to realise is that we need to start taking full points from that solid base."
The point leaves the Hammers 17th in the Premier League.