The Hammers dominated the 1-1 draw with QPR at Upton Park but could not breach Julio Cesar's defences until Joe Cole scored in the 68th minute to cancel out Loic Remy's 14th-minute opener on his QPR debut.
Allardyce's team have one win and five points in seven Premier League games.
He said: "Service and providing opportunities was great. Finishing, unfortunately, let us down.
"The bottom line is, as always, if you don't finish your chances you pay the penalty, and we paid the penalty by not finishing.
"We're in now our worst run for picking up points at the minute and that's not suggesting that our performances have warranted so few points. Our problem is our frontmen don't score enough goals to win us games of football we should win."
Marouane Chamakh saw two good headed opportunities saved by Cesar before he was replaced by Carlton Cole, whose header led to Joe Cole's equaliser.
It was Chamakh's full debut following his loan signing from Arsenal and, although the Moroccan will not be available to face his parent club on Wednesday night, Allardyce is convinced he will soon make the most of his opportunities.
"When you've got strong headers of the ball and you put 46 crosses in like we did you're giving them the right service," Allardyce added.
"Hopefully that will turn into him scoring a few more goals for us, because that's been our problem."
- Sports & Recreation