Allardyce's men have won just one of their last nine Premier League outings and were under pressure for large parts of the game at Upton Park.
The London club have slipped to 18th, only one point above the relegation zone, and have failed to score in five of their last eight top-flight matches.
"(We were) not at our best, that's clear for us all to see," a disappointed Allardyce told Sky Sports.
"Our in-possession work made life extremely difficult for us.
"At times, we never got the crowd excited and never got enough quality into their box and ended up with a 0-0 draw."
The West Ham boss did find some positives, however, citing his side's defensive effort, having only conceded 19 goals in the league.
"I point to the one thing we've done well this season and that's clean sheets," he added.
"We've built our base superbly well and the lads have to realise if you want to take points you need to score a goal.
"It's remarkable that with a defensive record like that we're in the bottom four area, not in mid-table."
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